Arrange the asparagus in a microwave-safe dish, cover and microwave on high until crisp-tender, about 2 minutes. (If you don?t have a microwave, you can steam the asparagus instead.) Brush asparagus with 1 tablespoon of the oil.
Heat a grill pan over medium heat. Grill the asparagus, flipping occasionally, until tender and lightly charred, about 5 minutes. Cut asparagus in half crosswise and then slice on the bias into 1-inch pieces. Sprinkle with salt and pepper.
Heat the remaining 1 tablespoon of oil in a large skillet over medium-high heat. Add the peppers and cook, stirring frequently, until tender and slightly charred, 8 to 10 minutes. Transfer to a bowl and stir in 1/2 teaspoon salt and a few grinds of pepper.
Lay a tortilla on a work surface and top evenly with 1/2 cup shredded cheese. Add 1/4 of the asparagus and 1/4 of the peppers. Fold tortilla in half to enclose fillings. Repeat with remaining tortillas and ingredients.
Melt 1/2 tablespoon of the butter in a large non-stick or cast-iron skillet over medium heat. Cook the quesadilla, flipping once, until the cheese is melted and it is golden brown on both sides, about 3 minutes per side. Remove to a cutting board and repeat with the remaining quesadillas.
Cut into triangles and serve topped with guacamole, salsa, chopped scallions and sour cream.
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