Place all ingredients into the bowl of food processor except for olive oil. Pulse for 15 seconds or so and then turn the machine on and drizzle in olive oil until desired consistency is reached. Store in refrigerator in an airtight container.
for the quesadillas-
In a large skillet, heat olive oil over medium heat and saute zucchini and baby eggplant until crisp-tender, 5-7 minutes. Remove from skillet and return to heat.
Spread pesto evenly on two tortillas. Sprinkle cheese over top of the pesto and then line cooked vegetables on half of the tortilla.
Melt 1 teaspoon of butter in skillet and place open quesadilla into the hot pan. Cook until the bottom of quesadilla has browned and cheese has melted. Fold tortilla in half to cover the veggies and press down lightly to press them into the melted cheese, so they stay in place. Repeat with another tortilla. Serve warm.