Preheat your oven to 375°F. Peel and devein the shrimp, then season with salt and pepper. Heat a large skillet over medium-high heat, add the shrimp, and cook for 3 minutes or until they are pink. Drain and set aside.
Place one of the tortillas on a flat surface and spread half of the salsa over it. Sprinkle with half of the taco seasoning, followed by half of the cheese, and then place the cooked shrimp on top. Place the second tortilla on top and press down lightly to seal.
Spray a baking dish with non-stick cooking spray, then carefully transfer your chimichanga to the dish and spray with non-stick cooking spray again. Bake for 20 minutes or until the chimichanga is golden brown and crispy.
Meanwhile, make the green chili sauce. Heat a medium saucepan over medium heat, and add olive oil and butter. When melted, add flour and stir to combine. Add the chicken broth, diced green chiles, cumin, salt, and pepper. Simmer for 5 minutes or until thickened.
Add the sour cream and cheese to the saucepan and stir until everything is combined and melted. When your chimichanga is ready, slice it and serve it with the green chili sauce.