Preheat the oven to 200 degrees F. Pierce the sweet potato a few times with a fork and microwave until soft, 7 to 10 minutes. Let cool slightly, then remove the skin and mash the flesh with a fork; set aside.
Heat 1 tablespoon butter in a large nonstick skillet over medium-high heat. Add the pork, chile powder and 1 teaspoon salt and cook, breaking up the meat, until browned, about 3 minutes. Add the garlic, sweet potato and scallions and cook, stirring, 2 more minutes. Add the cilantro and season with salt. Transfer the mixture to a bowl.
Wipe out the skillet; add 1/2 tablespoon butter and melt over medium-high heat. Add a tortilla, spread one-quarter of the pork mixture on one half and top with 1/2 cup cheese. Fold the tortilla over the filling and cook until the quesadilla is golden, 1 to 2 minutes per side. Transfer to a baking sheet and place in the oven to keep warm. Repeat to make 3 more quesadillas. Cut into wedges and serve with pickled jalapenos and sour cream, if desired.