In a large skillet, heat 1 tbsp. of the oil over medium heat. Once hot, add the peppers and onions and cook, stirring often, until they have begun to soften, about 3-4 minutes. Stir in the garlic and spinach and cook, stirring often, until the spinach wilts.

Add the black beans and seasonings to the skillet and cook just 2 or so minutes more, then remove from heat and transfer the bean mixture to a large bowl.

Stir the cilantro, lime juice and cheese into the bean mixture. Return the skillet to the heat and add the additional 2 tbsp. of oil to it.

Prepare the quesadillas by placing 1/4 of the bean and cheese mixture over one half of each tortilla, then fold the other half over it, so it's a half circle.

Once the oil is hot and shimmering, add the quesadilla carefully to the skillet. Cook for 2-3 minutes, or until golden, then flip it carefully and cook the other side for 2-3 minutes, until golden and the cheese is all melted.

Slice into thirds using a large, sharp knife and serve immediately.