Heat a large non-stick skillet over medium-high heat and add 2 t. olive oil. Add asparagus spears and saute until crisp-tender, about 5 minutes. Remove pan from heat and turn heat to medium.
While asparagus is cooking, spread the garlic and herb cheese on one half of the tortilla. Top with the cooked asparagus and sprinkle the mozzarella cheese on top of the asparagus.
Fold quesadilla in half, place pan back on burner and grill first side of quesadilla until nicely browned... start checking after 3-4 minutes if it's ready to turn. Brush the remaining teaspoon of olive oil on the top half of the cooked quesadilla. Flip quesadilla and grill the second side.
Remove from pan and slice with a knife. Drizzle with balsamic glaze