Heat a skillet over medium heat. Add bacon slices and cook until crispy. Remove and drain on paper towels, then crumble into pieces.
Whisk eggs, milk, salt, pepper, and paprika in a bowl. Scramble in a pan over medium-low heat with butter or oil until cooked but still slightly moist. Add green onions if desired.
Lay a tortilla flat, sprinkle half the cheese, add scrambled eggs, bacon, then remaining cheese. Top with another tortilla.
Heat a skillet over medium heat with butter or oil. Cook quesadilla 2–3 minutes per side until golden brown and cheese melts. Press lightly with a spatula.
Let rest 1 minute, slice into wedges, and serve with salsa or hot sauce.