Lay out a tortilla and cover half with 1/4c cheese and 1/4c salsa. Fold the other half over, pressing down. Repeat with remaining tortillas. Heat a wide saute pan over medium-high heat. Heat 2 tablespoons of the oil in the pan and put in 1 tortilla. After 3-4 mins., carefully flip over. (Bottom side should be golden brown.) Continue cooking for 3-4 more mins, then remove the quesadilla and keep it warm. Repeat with remaining tortillas, adding oil as needed.
Cut into 4 wedges each.