Heat the oil in a 10-inch skillet over medium-high heat. Add the shrimp and cook for 2 minutes or until they’re cooked through, stirring often. Stir in 1 cup salsa and cook until the mixture is hot and bubbling.
Spread half the shrimp mixture on each of 2 tortillas. Top each with half the cheese and half the beans. Brush the edges of the tortillas with water. Top with the remaining tortillas and press the edges to seal.
Heat a 12-inch nonstick skillet over medium-high heat. Cook the quesadillas one at a time for 5 minutes or until they’re golden on both sides and the filling is hot. Cut the quesadillas into wedges and serve with the remaining salsa.