Sauté Mushrooms: Heat 1 tbsp of olive oil in a skillet over medium-high heat. Add mushrooms in a single layer. Cook undisturbed for 3-4 mins.
Season: Stir in thyme, oregano, salt, and pepper. Continue cooking until mushrooms are golden brown. Add minced garlic and cook for 1 more minute. Drizzle with lemon juice and remove from pan.
Prepare Bread: Brush one side of each bread slice with the remaining olive oil.
Assemble: On the non-oiled side of 2 slices, layer half the mozzarella, the mushroom mixture, the feta, and the remaining mozzarella. Top with the remaining bread slices (oil side out).
Grill: Wipe the skillet clean. Place sandwiches in the pan over medium heat. Grill for 3-4 minutes per side until the bread is golden brown and the cheese is fully melted.
Serve: Let rest for 1 minute, slice diagonally, and enjoy!