Heat 1 teaspoon olive oil in a large nonstick skillet over medium-high heat.
Add the onion and garlic, and saute for 3 minutes. Stir in 1/2 cup salsa, cumin, and beans, and bring to a boil. Reduce heat, and simmer for 5 minutes or until thick. Mash the bean mixture slightly with a potato masher.
Remove from heat; stir in the cilantro and goat cheese.
Spread the bean mixture evenly over 4 tortillas; top each with 1 tortilla, pressing gently.
Heat 1/4 teaspoon olive oil in pan over medium-high heat.
Add 1 quesadilla, and cook for 2 minutes on each side. Repeat the procedure with the remaining olive oil and quesadillas.