Heat the oven to 425°F and brush an 18-by-13-inch rimmed sheet pan with 1 tablespoon oil. Mix chicken, corn, dry spinach, cheese, jalapeños, cumin, garlic powder and salt in a bowl.
Arrange 6 tortillas around the pan edges with roughly half of each hanging over the rim, overlapping to cover the sides. Place 1 tortilla in the center to cover the remaining bottom gap.
Spread filling evenly across the base. Place the last tortilla over the center of the filling, then fold all overhanging tortilla halves inward to enclose it.
Brush the top with remaining oil, cover with foil and set a second clean sheet pan directly on top as a light weight. Bake for 20 minutes.
Remove the upper pan and foil and bake for 8 to 10 minutes more until the tortillas are golden and the center reaches 165°F.
Rest for 5 minutes, cut into 12 rectangles and serve 2 per portion with 2 tablespoons salsa.