In a medium skillet, heat 2 teaspoons olive oil on medium heat. Add spinach and cook just until wilted. Remove any excess liquid, and add beans, egg whites, and salt. Scrambled the mixture until eggs are cooked through.
Carefully wipe out the skillet and heat the remaining one teaspoon of olive oil on medium heat. Once hot, place one tortilla in the oil. Quickly sprinkle half of the spinach and egg mix and top with half of the cheddar and half of the mozzarella cheese. Place a second tortilla on top. When cheese begins to melt and the bottom tortilla has begun to brown, carefully flip the quesadilla to cook the second side. When the second is browned remove from the pan and let cool slightly before cutting and servings. Repeat the process with the remaining tortillas and ingredients.