Preheat oven to 475 degrees. Place 2 flour tortillas (8 inches each) on a rimmed baking sheet and sprinkle with Monterey Jack cheese. Bake until cheese is melted and tortilla edges are just beginning to crisp, about 3 minutes.

Meanwhile, in a small bowl, combine shrimp, vegetable oil and chili powder. Season with coarse salt and ground pepper.

Divide shrimp mixture and scallions between the tortillas. Bake until shrimp is opaque throughout, about 4 minutes.

Sprinkle quesadillas with cilantro and cut each into 6 wedges. Serve with lime wedges.