Preheat your oven to 350°F (175°C).
In a large skillet, heat the olive oil over medium heat. Add the shrimp and season with garlic powder, onion powder, chili powder, cumin, salt, and pepper. Cook until the shrimp are pink and opaque, about 3-4 minutes. Remove from heat.
In a mixing bowl, combine the sour cream, half of the shredded cheese, and half of the salsa verde. Stir until well combined.
To assemble the enchiladas, place a few shrimp in the center of each tortilla. Add a spoonful of the sour cream mixture on top of the shrimp, then roll the tortilla tightly and place it seam-side down in a greased 9x13-inch baking dish.
Repeat with the remaining tortillas and shrimp. Once all enchiladas are in the dish, pour the remaining salsa verde over the top and sprinkle with the remaining cheese.
Bake in the preheated oven for 20-25 minutes, or until the cheese is bubbly and golden.
Remove from the oven and let cool for a few minutes. Garnish with chopped cilantro if desired before serving.