Stir together the mashed potatoes, bacon, and green onions. Spread the mashed potato mixture onto one side of half of the tortillas, spreading to within 1/2 inch of the edges. Sprinkle the shredded cheese on top of the mashed potatoes and top with the remaining tortillas. Lightly butter each side of the quesadillas.
Preheat a large skillet over medium heat. Place a quesadilla into the preheated pan, and cook until golden brown and crispy, then turn over, and continue cooking on the other side until browned, 2 to 3 minutes per side. Repeat with remaining quesadillas. Serve with salsa and sour cream.