In a food processor or high-powered blender, combine the pine nuts, spinach, basil, garlic, parmesan, lemon juice, salt, and olive oil. Pulse/blend until smooth, about 60 to 90 seconds, and stop to scrape down the sides as needed. Drizzle in more olive oil as needed to promote blending. Remove the pesto from the blender and transfer to a jar or bowl.
Preheat a large skillet over medium-high heat. Place a tortilla into the skillet and heat for a minute on each side. Spread one to two tablespoons of pesto on top of the tortilla. Leave about 1/2-1 inch around the edges of the tortilla (the pesto will spread out as it melts). Sprinkle the cheese on one half of the tortilla. Cook for a couple of minutes until the cheese starts to melt around the edges. Use a fork to flip the other half of the tortilla over the side with the cheese and press it into the melted cheese around the edges. Cook for another minute or two until the cheese is melted through. Remove from heat and repeat with the rest of the tortillas.
Slice the quesadillas in half before serving, and enjoy!
You can use different size tortillas for the recipe, but you will need to adjust how much pesto and cheese you add.
Make the pesto in advance to save time. It will last in an airtight container in the fridge for about a week.
If you don't have pine nuts, you can sub pecans, sunflower seeds, or almonds.
Look for a parmesan cheese that is made with vegetarian rennet if you need these to be strictly vegetarian.