Preheat oven to 400 degrees F.

Heat a large skillet over medium-high heat and add the olive oil. Once oil is warm stir in the minced garlic and mushrooms and reduce heat to medium-low.  Sprinkle with a small pinch of salt.  Continue to cook mushrooms until soft and tender, about 5-8 minutes, stirring occasionally. Add the balsamic vinegar and stir again.

Add the spinach to the same skillet in two batches; allowing the first batch to wilt slightly before adding the second batch.  Continue to cook until spinach is completely wilted and liquid has evaporated (soggy quesadillas are no good). Season with salt and pepper to taste.

Brush one side of the tortillas using the remaining tablespoon of olive oil.  Place 3 tortillas, oiled side down, on a large baking sheet lined with parchment paper.  Layer each tortilla with a thin layer of mozzarella cheese, a sprinkle of crumbled goat cheese, sauteed spinach and mushroom, and a final layer of goat cheese and mozzarella cheese. Top with the remaining 3 tortillas, oiled side up, and place in the oven until cheese is melted and tortillas are golden, flipping once (approximately 8-10 minutes).

Cut into quarters and serve.