I would use a corn starch slurry. 1:1 ratio with water

gravy more complimentary for the potatoes.

Corn starch best for gravy. Mix with cold water first Boil as jou and mix in slowly

The sour cream would turn it towards stroganoff imo.

Either would be great

Soooo good. I strain the juices into a bowl with a spout and make a roux on the stovetop, slowly adding the juices to make gravy. A quicker thickening is bringing your broth to a simmer and adding a little slurry made of cornstarch and water, stirring constantly as it thickens.

Add: Oops, got distracted mid-typing and see others already posted about cornstarch.

Making then icorporating a roux into sauces and gravies might take some practice though. But it's a basic building block and technique to have at hand.

It works pretty well.

he usually starts with a butter/flour roux and adds milk or stock or broth until it's the desired consistency

Maybe half a can if small amount of liquid
.. maybe add some red wine or beer too

And I usually do “shortcut gravy” - cook with 1 cup beef stock, 1 envelope onion soup mix and a can of cream of celery (DH hates mushrooms).
Some roasts, especially eye roast, never get fall-apart tender. If that happens I slice down the meat and put it back in the crockpot with the gravy for .5 to 1 hour before serving. The extra moisture makes it tender.

and coat with flour before you sear. use lots of chopped onion (can saute them too), both will thicken juices as meat cooks.

for now either corn starch ("dissolved"in a bit of cold water before adding to juices then cooking for a few minutes) or make a light roux (flour cooked in some kind of fat) then add liquid

for sure not much fat on an eye of round. that is a funny cut. when cooked right it can be a "poor man's" rib roast. it can actually be roasted dry and quickly to be served as thin sliced rare roast beef. it isn't especially tender but when sliced thin it can be quite good. while it doesn't have marbling or external fat, it also doesn't have a lot of the connective tissue that makes braised meats come out so good when cooked low, slow and with extra moisture. that stuff melts and also helps to thicken your gravy.