In a large skillet, heat olive oil over medium heat and add red onion. Sauté until softened, about 4 minutes. Add peppers and cook until tender, about 6 minutes. Remove from skillet.
In same skillet, add crumbled or chopped sausage and cook until slightly browned and cooked through.
Place 4 tortillas on work surface, spread ¼ cup of cheese on half of each tortilla. Top with 1/4 of the cooked chorizo, 1/4 of the onion and pepper mixture, and top with remaining cheese. Sprinkle each with 1/2 tablespoon of the cilantro and fold the other half of the tortilla over.
Heat a large non-stick skillet over medium heat. Add ½ Tablespoon butter to skillet. Lightly brown 1 quesadilla on each side until cheese is melted (about 1 ½ minutes per side). Repeat with the remaining quesadillas, adding remaining butter after the second quesadilla.