Preheat the oven to 350°F (175°C).
Heat 1 tbsp olive oil in a large skillet over medium-high heat. Add the diced onion and diced jalapeños and sauté 2–3 minutes until the onion is translucent.
Add 2 1/2 cups shredded cooked chicken to the skillet and cook 1–2 minutes to warm through.
Pour in 1/2 cup of the chicken broth, 1/2 cup heavy cream, 1/2 tsp paprika, and 1/2 tsp salt. Stir to combine and heat through, then remove from heat and set the chicken mixture aside.
In a separate large skillet, melt 4 tbsp butter over medium heat. Whisk in 1/4 cup flour until a paste forms, then slowly whisk in the remaining 1 1/2 cups chicken broth until smooth.
Whisk in the remaining 1/2 cup heavy cream and 1 cup sour cream until combined.
Stir in 2 cups of the shredded Monterey Jack cheese and the remaining 1/2 tsp paprika until the cheese melts and the sauce is smooth. Remove from heat and fold in 2 diced avocados; set the cheese sauce aside.
Warm the corn tortillas until soft and flexible. Place a portion of the chicken mixture in the center of each tortilla, top with a few slices of the remaining avocado, and roll the tortilla. Place seam-side down in a 9x13-inch baking dish.
Pour the cheese sauce evenly over the rolled enchiladas, then sprinkle with the remaining 1 1/2 cups shredded Monterey Jack cheese.
Bake in the preheated oven for 20–25 minutes, until heated through and the cheese is melted and bubbly.
Remove from oven and serve; top with sour cream or salsa if desired.