In a Ziploc bag, combine mushrooms, balsamic, and ¼ cup olive oil. Seal and marinate at room temperature for 20 minutes.

Season mushrooms with 1 tablespoon salt and pepper. Cook mushrooms on a preheated grill or grill pan for 6 to 8 minutes per side or until softened and nicely browned.

While mushrooms are cooking, in a small bowl whisk together remaining ½ cup olive oil, remaining ½ teaspoon salt, garlic, and oregano. Brush both sides of each slice of bread with garlic oil and grill 2 to 4 minutes or until lightly toasted and warmed.

Assemble each “burger” by topping a slice of bread with 2 slices of tomato, 2 mushroom caps, a basil leaf, and another slice of bread.