Marinate Mushrooms: In a bowl, whisk olive oil, balsamic vinegar, garlic, paprika, salt, and pepper. Brush this mixture onto both sides of the mushrooms. Let them marinate for 20 minutes.
Preheat Grill: Heat your grill or grill pan to medium-high.
Grill Mushrooms: Place mushrooms on the grill, gill side down. Cook for 4-5 minutes per side, until tender and lightly charred.
Prepare Buns and Toppings: Toast burger buns on the grill for 1-2 minutes. Layer lettuce, tomato, grilled mushrooms, and avocado slices on each bun.
Assemble and Serve: Add optional cheese and secure the top bun. Serve immediately with your favorite sides.