You're welcome,
I'll try to break this down into segments, so you can understand a few of various methods I've seen used, or partook of in myself:
OK, for the basic roast, without a rack in the DO, it will cook a bit faster than if elevated off the bottom and using a few ounces of added liquids for steam.
If roasting, and wanting it med/rare, you could add pieces of carrots, celery, taters, parsnip, turnips, beets (whatever you like). Add those items within the first two hours of cooking the meat, then, they should be fairly tender when the meat is nearing finished temps. Cut them at least 1/2 to 3/4 thick. Sliced on the bias adds a nice rustic touch. Maybe probe before adding veggies to be sure it has reached at least 85-90* I/T before adding veggies. Depending on how it all comes together, the low and slow can create a tender but firm vegetable...not mushy. Simple herbs and spices rubbed onto the meat such as thyme, rosemary, garlic, cracked black pepper and a bit of salt (if you like) will go far, as the veggies add tons of flavor to the meat and the juices. I generally use less salt with leaner cuts of meat.
When resting the eye, you could remove everything except the liquids from the DO (platter and cover) and finish the liquids as au jus, or as a gravy on the stovetop (would be excellent flavors for either one with all the veggie and beef flavors in it).
For gravy, you need some type of fat in the hot liquids, either from the meat or added vegetable/canola/corn/olive oil, or butter. If it's a realy lean cut as the eye round, you may need to add a few Tbls of fat, either before of after cooking the meat. Then, add flour/and or corn starch to cold water and mix well (I prefer just flour). A fairly thick gravy starter will work fine, say, 3 Tbls flour to 3/4 cup cold water. Combine gravy starter into simmering liquid base in saucepan/skillet/pot/DO used to cook the meat, and continuously stir. Gravy will thicken as it heats through. If you want a more intense flavor in the gravy, reduce the liquids (simmer uncovered to evaporate excess liwuids, leaving a higher concentration of suspended solids) before adding the gravy starter. If the you find the gravy to be too thick, just stir in a little water at a time unitl it reaches your desired consistency. If too thin, make more starter and stir in while still simmering over heat. Salt and add additional seasoning to your taste. Usually the salt is a bit light at first, but that depends on how much salt is on the meat and anything else in the pot. That's my basic gravy process...works for roasted chicken, pork or beef. Oh, if there is excessive amount of fat in the liquids, I just skim them off with a small ladle, or even a soup spoon will work (prior to simmering to start the gravy/au jus) until there is just a thin layer on top of the water...then it's ready to go.
As for the gravy, many folks haven't nailed down the basic concept, so they don't like to mess with it for fear of screwing it up. As you can see, it isn't dificult to make, so I would recommend it, especially if veggies get tossed into the equation. If I can make it? Can't be very hard! LOL!!! And, there's nothing quite like a roasted side of veggies with a nice ladle of gravy poured over the top, and I haven't even begun speaking about the meat...mmm-mmm-mmm.
For au jus, you can reduce it to intensify the flavors as described above, then just a bit of instant coffee (decaf or leaded) stirred in will top it all off. Add small amounts, stir and taste...stop when you like it. Can't really say how much most folks like, and without measuring the base liquids makes it tougher, so to your taste is the best route.
Taste is everything with sauces, gravies, etc. Texture comes second, IMHO...texture adds character. You know the old TV commercial for a gravy mix when the old guy says..."yeah, but where are the lumps?"...as his wife frowns upon him with looks that could kill...ha-ha!!! Anyway, I think mixes are over-rated...home-made rocks!
For stewing, you'd just cut it up into chunks and add the veggies after searing the flour-dredged meat in oil/butter, adding water, herbs and spices. There are varying methods for creating the stew's gravy/sauce, from adding the mix liquids with the veggies after the meat has been seared and allowing the slow cooking to do the rest, to waiting until just prior to serving and preparing as described above for gravy making. Stewing is pretty easy, but not the same as having that nice slice of beef on your plate along side all those great tender roasted veggies.
Braising is more used as a tenderization method for stovetop cooking...probably not the route you want, especially if med/rare is your liking. Good for getting tougher cuts of meats (or whole chickens) prepared for soups. I do love a nice beef, vegetable and potato soup, I will admit.
Sounds like a great meal coming your way way, no matter which route you go. I have found that when trying new (to me) dishes or methods, keeping it simple is the best way to start. Just stick with the basics, and the flavor profiles you know and like and you'll have a nice taste of heaven on your plate.
Jee-whiz...just thinking about all this while writing it up has really got my wheels turning for an upcoming large family gathering next summer...hmmmmmmmmmmm.
Eric