Heat a large skillet over high heat and cook the corn in 1 teaspoon oil until browned in spots, 4 to 5 minutes.
Transfer the corn to a bowl and mix it with the pulled pork and salsa verde.
Lay out four tortillas and divide half the cheese, the pork mixture, scallions and remaining cheese among them.
Top with the remaining tortillas and press gently.
Brush the skillet with some of the remaining oil and cook one quesadilla at a time over medium heat until browned, about 3 minutes per side.
Rest each quesadilla for 2 minutes, cut into wedges and serve with sour cream and lime.