Put the tomatoes, chili powder, garlic, 1/2 teaspoon salt and 2/3 cup water in a small saucepan. Bring to a simmer and cook 10 minutes, breaking up the tomatoes with a spoon. Add the chicken and cook, flipping once, until cooked through, 8 to 9 minutes per side. Transfer the chicken to a plate, shred it, then return it to the sauce. Add salt and pepper to taste.
Lay a tortilla on a work surface and top evenly with 1/2 cup of the Monterey Jack. Add one-quarter of the shredded chicken in sauce and some chopped chipotle chiles and adobo sauce, depending on how spicy you like it. 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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