Roast poblano peppers in the oven at 400°F for 25 minutes, flipping halfway. Let cool, then peel skins, remove stems and seeds, and either slice into strips or cut into halves for stuffing.

Shred Oaxaca and Monterey Jack cheese. Mix together.

Heat skillet or griddle over medium heat. Lay a tortilla directly on the hot surface and spread a thin layer of butter on the top side. Flip tortilla so buttered side is down.

On one half of the tortilla, place roasted poblano strips or half a poblano pepper. Add ½ cup of the cheese mixture. Fold tortilla in half and press gently.

Cook until bottom is golden and cheese begins to melt, about 2 to 3 minutes. Flip and cook the other side until golden brown and crisp. Repeat with remaining tortillas.

Cut quesadillas into triangles and serve hot.