Preheat your oven to 350° F. Wipe mushrooms clean with a damp cloth and pull out the stems and discard. Toss the cleaned de-stemmed mushrooms with 5 tablespoons of olive oil, balsamic vinegar, salt, and pepper. Spread out on a sheet pan and bake for 30 minutes. Set aside and cool.
Slit the Italian sausage and remove casing. Crumble in a heated pan and sauté until golden brown. Break up into small pieces while it is cooking. Set aside and cool.
Add the remaining 2 tablespoons of olive oil in a sauté pan and add the onions. Cook until dark and caramelized, about 15 to 20 minutes. Then add in the garlic and cook for a minute.
Now add the cooked sausage, onions and garlic, cream cheese, salt and pepper, and 3 oounces of shredded Asiago cheese to a bowl and mix well with your hands. Break apart any large pieces of sausage.
Heat your oven to 375° F. Line up your mushrooms in a greased baking dish with the core side facing up. Stuff each mushroom with a generous portion of the creamy sausage mixture. Top the mushrooms with the remaining Asiago cheese.
Bake your mushrooms for roughly 45 minutes or until the cheese on top is golden brown. (This dish can be made up to 3 days ahead of time and put in the cooler until you are ready to put it in the oven.)