Spread butter evenly over one side of each tortilla.
Heat a large skillet over medium heat. Place one tortilla in the skillet with the buttered side facing down.
Sprinkle half of the Monterey Jack, half of the extra sharp cheddar, and half of the Gouda evenly over the tortilla, leaving a small border around the edge.
Cook until the underside is golden brown and the cheese has melted. Fold the tortilla in half and remove from the skillet.
Repeat with the remaining tortilla, butter, and cheeses.
Let the quesadillas rest for 2 to 3 minutes before slicing.
Cut each quesadilla into 4 wedges and serve immediately with your favorite dipping sauces, if desired.
Notes
Freshly grated cheese melts more smoothly than pre-shredded cheese for the best texture.
Keep the heat at medium to allow the cheeses to melt completely before the tortilla becomes too dark.
Feel free to substitute your favorite melting cheeses while keeping the total amount of cheese the same.
A pizza cutter makes clean, even wedges that are easier to pull apart.