Preheat the oven to 450°. Lightly brush 2 large baking sheets with oil and heat in the oven for 5 minutes. Lightly oil 1 side of each tortilla and place them, oiled side down, on the baking sheet. Layer the cheese and turkey on the tortillas and bake until the cheese is melted and the bottoms of the tortillas are golden, 4 to 5 minutes.
Meanwhile, in a large bowl, mix the olive oil with the lime juice and sour cream. Add the arugula and tomatoes, season with salt and pepper and toss well. Transfer the tortillas to a work surface, top with the arugula salad and fold in half to close. Cut each quesadilla into 3 wedges and serve right away with sour cream, hot sauce and lime wedges on the side.