Heat a large non-stick skillet over medium heat.
Place one flour tortilla flat in the skillet.
Sprinkle the shredded cheddar cheese evenly over the tortilla.
Sprinkle the shredded Monterey Jack cheese evenly over the cheddar cheese.
Place the second tortilla on top, pressing down gently.
Melt the butter in the skillet around the edges of the tortilla stack.
Cook for 2 to 3 minutes until the bottom tortilla is golden brown and the cheese starts to melt.
Carefully flip the quesadilla using a spatula and cook for another 2 to 3 minutes until the second side is golden brown and the cheese is fully melted.
Remove the quesadilla from the skillet and let it cool for 1 minute.
Cut the quesadilla into 4 equal wedges and serve immediately.