In a 10- to 12-inch nonstick frying pan over medium-high heat, stir garlic in olive oil often until limp, about 1 minute.
Add shrimp and stir often until pink on the outside, 2 to 3 minutes.
Add lime juice and stir occasionally until most of the liquid has evaporated and shrimp are opaque but still moist-looking in center of thickest part (cut to test), about 3 to 5 minutes. Stir in all but 2 tablespoons green onions and the cilantro and add salt and pepper to taste.
Lay 2 tortillas flat on a 14- by 17-inch nonstick baking sheet. Divide half the shrimp mixture between tortillas and spread to within 1/2 inch of edges.
Sprinkle a third of the cheese over shrimp.
Lay another tortilla on each stack and top equally with remaining shrimp mixture and another third of the cheese. Cover with remaining tortillas and sprinkle remaining cheese over the top.
Bake in a 400 regular or convection oven until cheese is melted around edges of stacks and beginning to brown on top, 10 to 12 minutes. With a wide spatula, transfer stacks to plates.
