Heat 2 teaspoons of the oil in a large skillet over medium heat. Add the shallots and cook until they brown and soften, about 3 minutes. Add the spinach with whatever water clings to the leaves and season with salt and pepper. Increase the heat to high and stir, incorporating any browned bits from the bottom of the pan; cover and cook until the spinach is wilted, about 1 minute. Transfer to a bowl.
Heat the remaining 1 tablespoon oil in the same skillet over medium-high heat. Add the bell peppers and cook until tender and slightly charred, 8 to 10 minutes. Season with salt and pepper.
Lay a tortilla on a work surface and top evenly with 1/2 cup of the Cheddar. Add one-quarter of the spinach mixture, one-quarter of the bell peppers and one-quarter of the beans. Fold the tortilla in half to enclose the fillings. Repeat with the remaining tortillas and ingredients.
Melt 1/2 tablespoon of the butter in a large nonstick or cast-iron skillet over medium heat. Cook a quesadilla, flipping once, until the cheese is melted and it is golden brown on both sides, about 3 minutes per side. Transfer to a cutting board and repeat with the remaining butter and quesadillas.
Cut into triangles and serve topped with sour cream, chopped scallions, guacamole and salsa.
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