Heat a medium size skillet on low to medium heat.
Add ½ of the butter and as soon as it melts, add one of the quesadillas. The idea is to cook each side just enough to melt the cheese.
Use a spatula to peek under the side that's touching the skillet to make sure it’s not getting too brown (it should be a light golden color).
As soon as the cheese starts to melt (on the side touching the skillet), carefully flip over the quesadilla to the other side (no need to add more butter at this point).
When the cheese starts to melt on the side of the tortilla that is touching the skillet, remove the quesadilla, cover with foil and set aside.
To the pan, add the rest of the butter and repeat the cooking process for the other quesadilla.
Cut the quesadillas into quarters and serve right away while warm.