Preheat the oven to 350°F (175°C).
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the diced onion and 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 combine.
Pour in 1/2 cup of the chicken broth, 1/2 cup heavy cream, 1/2 teaspoon paprika, and 1/2 teaspoon salt. Stir and heat through, then remove the chicken mixture from the heat and set aside.
In a second large skillet, melt 4 tablespoons butter over medium heat. Whisk in 1/4 cup all-purpose flour until combined and slightly clumpy, then slowly whisk in the remaining 1 1/2 cups chicken broth until smooth and slightly thickened.
Stir in the remaining 1/2 cup heavy cream and 1 cup sour cream until smooth.
Add 2 cups of the shredded Monterey Jack cheese and the remaining 1/2 teaspoon paprika to the sauce; stir until the cheese melts and the sauce is smooth.
Peel and dice 2 of the avocados and fold them into the cheese sauce, then remove the sauce from the heat and set aside.
Warm the corn tortillas in the microwave or on a griddle until soft and pliable. Place a portion of the chicken mixture down the center of each tortilla, top with a couple slices of the remaining avocado, and roll tightly. Place seam-side down in a 9x13-inch casserole dish.
Pour the cheese-avocado sauce over the rolled enchiladas and 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.
Let the enchiladas rest a few minutes before serving. Optional: top with a little sour cream or serve with salsa.
