In a large skillet, heat olive oil over medium heat. Add minced garlic and chopped onion, sautéing until soft and fragrant, about 3-4 minutes.

Add shrimp to the skillet. Cook for 2-3 minutes on each side until pink and opaque. Remove shrimp, chop, and mix with green chiles and cilantro in a bowl.

In a saucepan, melt butter over medium heat. Whisk in flour to create a roux, cooking for about 1 minute. Gradually add milk, whisking until thickened, about 5 minutes. Stir in sour cream, cumin, chili powder, and half of the Monterey Jack cheese.

Preheat oven to 375°F (190°C). Warm tortillas until pliable. Spoon shrimp filling into each tortilla, roll tightly, and place seam-side down in a greased baking dish.

Pour creamy sauce over enchiladas and sprinkle with remaining Monterey Jack cheese. Bake for 20-25 minutes until cheese is melted and golden.

Allow to cool slightly, garnish with chopped cilantro, and serve with lime wedges.