Heat olive oil and 1 teaspoon of butter over medium-high heat. Add butternut squash for about 5-7 minutes or until squash is just about fork tender. Add spinach leaves for about 3 minutes more or until spinach has wilted. Remove from heat. To assemble each quesadilla. Butter one side of the tortilla and place it butter-side down in a clean pan that has been heated over medium heat.

Spread about 1/2 cup of butternut squash and spinach mixture over the tortilla. Sprinkle about 1/4 cup of cheese over the top of the squash and spinach. Butter one side of a second tortilla and place it, butter-side up on top of the cheese. When the bottom layer is toasty and the cheese has begun to melt (about 1-2 minutes), flip the tortilla over and toast the other side. Remove from pan and repeat process to make the rest of the quesadillas. Cut quesadillas into triangles using a pizza cutter.