On a piece of parchment paper, brush one of the whole tortillas with well softened butter. Flip over so that the buttered side is down.
Add 2 ounces of the cheese (about a fourth) to one side of the tortilla. Sprinkle with Italian seasoning (to taste).
Place one of the tortilla halves on top of the cheese. Repeat another layer of 2 ounces of cheese and Italian seasoning.
Fold over to close, butter side will now be up.
Cook in a hot skillet over medium-high heat for 3-4 minutes per side, or until golden brown and cheese is melted.
Repeat for second quesadilla.
Notes
The type of cheese you want to use is solely up to you here. A blend of Monterey jack, cheddar, and mozzarella is what you'd typically find in prebagged Tex-Mex cheese. You can use all of one cheese or mix and match them, but I would always suggest using a block of freshly shredded cheese over store-bought. Store-bought shredded cheese contains anti-caking agents which prevent them from melting well and can sometimes cause the cheese to have a grainy texture.
We love the flavor Italian seasoning adds to this quesadilla, however, you can certainly omit it if desired or substitute it with whatever seasonings you like. Try paprika or cayenne pepper to spice it up a bit. Using a seasoned or flavored cheese like jalapeno pepper cheese will add flavor all on its own.