Dice onions and shallots
In a pan over medium-high heat, add 2 tbsp olive oil, diced onions and shallots, a splash of water (about 3 oz), and a sprinkle of salt. Stir occasionally
Once water evaporates, turn heat to low. Stir occasionally to ensure it does not burn.
While onions are caramelizing, prep mushrooms, occasionally tending to mushrooms to stir. Wash mushrooms well, then, using a spoon, scoop out the stems and gills. Place hollowed mushrooms into a baking dish and chop up stems and gills.
After about 1.5 hours of cooking down the onions, add in the chopped mushrooms, minced garlic, thyme, another sprinkle of salt and pepper and a drizzle of olive oil. Continue to stir occasionally and allow to cook down for about 45 minutes.
Preheat oven to 425
Add balsamic vinegar to pan and, using a wooden spoon, scrape up anything on the bottom of the pan.
Stuff mixture into mushrooms and top with shredded cheese of choice or seasoned breadcrumbs.
Bake at 425 for 20 minutes, or until cheese is melted and top is golden brown