In a small bowl, whisk together olive oil, balsamic vinegar, and garlic.
Place mushroom caps in a single layer inside a large disposable zip top bag (use two bags if necessary) and pour the oil mixture in as well. Seal the bag tightly and turn it over, rubbing the mushrooms from the outside of the bag to ensure they’re coated in the marinade. Allow to rest for 15 minutes, turning the bag over once.
Remove the mushrooms from the bag and place them stem side down on a large rimmed baking sheet. Bake 10 minutes.
While the mushrooms are baking, prepare the VeggieMash according to package directions.
Remove the mushrooms from the oven and turn them over. Spread about 3 tablespoons of VeggieMash evenly onto the top of each mushroom cap. Top with 1 heaping tablespoon of cheese per mushroom. Return to the oven and bake an additional 10 minutes or until the cheese is melted and everything is hot.