Preheat oven to 400 degrees.
Combine minced garlic, olive oil, balsamic vinegar, salt and pepper in a small dish.
Place mushrooms into a gallon ziplock bag and pour balsamic mixture into the bag, seal it, and rotate to ensure mushroom caps are evenly coated.
Optional: Let marinate 15 minutes or longer.
Place portobello mushrooms on wire baking rack and set in the oven on middle rack. Bake for 15 minutes.
Top mushrooms with feta cheese, and bake for an additional 10 minutes. If there is marinade left over it can be drizzled on the mushrooms when adding feta.
Remove portobello mushrooms from the oven and let cool for 5 minutes and serve.