Combine all the ingredients for the rub, and coat the eye round roast with it. If the roast is large it can be cut in half to fit into the Instant Pot.
Heat a pan or the Instant Pot, and add some olive oil to it. Brown the roast on all sides and remove to a plate. Add the sliced vegetables to the pan, and saute until the onions are soft and translucent. Add the garlic and cook for a minute.
Deglaze the pan with the wine, and reduce by a third. If using broth just deglaze the pan. Add the 4 cups of beef broth. If doing this in a pan pour into the Instant Pot. Add the rack that came with the Instant Pot into the pot. Put the eye of round roast back in. Seal, and cook on high pressure for 45 minutes then follow with a 10 minute natural pressure release. For a more tender roast or if it is slightly larger than 4 pounds add 5 minutes to the high pressure time, and 5 minutes to the natural pressure release.
While the roast is cooking, slice 4 onions. Saute in olive oil, salt and pepper to taste until soft and translucent.
Once the roast is done remove from pot, and slice thinly. Put the Instant Pot on saute and add two tablespoons of butter until melted. Pepper the au jus gravy to taste.
Serve immediately on crusty bread, top with onions, and cheese. Serve with au just gravy for dipping.
Serve immediately, or refrigerate up to one week in an airtight container.