In a large skillet over medium heat, add 1 tablespoon of butter and diced onion. Sauté for about 3 minutes until the onion becomes translucent.

Next, add the chopped shrimp and cook for 4-5 minutes until they turn pink and opaque. Stir frequently and set aside to cool slightly.

In a medium saucepan, melt 3 tablespoons of butter over medium heat. Stir in 3 tablespoons of all-purpose flour, creating a roux for about 1 minute until golden.

Gradually add 1.5 cups of broth, whisking continuously to prevent lumps. Mix in 0.5 cup sour cream and 4 oz cream cheese until smooth.

Warm the tortillas briefly in the microwave for 10-15 seconds. Spoon a portion of the shrimp mixture into each tortilla, roll them up, and place seam side down in a greased baking dish.

Pour the creamy sauce evenly over the tortillas, ensuring each one is covered. Sprinkle 2 cups of shredded Monterey Jack cheese over the top.

Preheat your oven to 350°F (175°C) and bake the assembled enchiladas uncovered for 20-25 minutes until the sauce is bubbling and the cheese is golden.

Remove from the oven, let them rest for a few minutes before serving.