Preheat the oven to 400 degrees F.
Sprinkle the chicken breasts with salt and pepper and drizzle with the olive oil. Put on a baking sheet and bake until just cooked through, about 15 minutes. Let cool slightly, then shred the meat with 2 forks.
Roast the bell peppers and chiles directly on a gas burner (or directly under the broiler) until the skin is mostly black. Throw the peppers and chiles into a plastic storage bag and seal it. Let them steam inside the bag for 30 minutes or so. Core and seed, then scrape off the black skin. Chop and set aside.
In a large skillet over medium heat, saute the chopped onions and jalapeno in the vegetable oil until the onions are translucent, 2 to 3 minutes. Throw in the shredded chicken, then stir in 1 cup of the chicken broth and 1 cup of the heavy cream. Add 1/2 teaspoon of the paprika and some salt and pepper, then add half of the chopped roasted peppers and chiles. Stir the mixture around and let it cook for a couple of minutes, then set it aside.
In a separate skillet over medium-high heat, melt the butter. Sprinkle in the flour and whisk it together to combine. Cook, whisking constantly, for 1 minute. Then pour in the remaining 2 cups chicken broth, stirring constantly. Cook, stirring, until the mixture is smooth, 1 to 2 minutes. Then add the remaining 1/2 cup heavy cream, the remaining 1/2 teaspoon paprika and 1 1/2 cups of the grated cheese. Finally, stir in the sour cream and the rest of the chopped roasted peppers and chiles. If the sauce needs a little thinning, splash in as much broth as you need. Give the sauce a taste and add salt if it needs it (with all the cheese, it shouldn't need much).
Preheat the oven to 350 degrees F.
Wrap the tortillas in paper towels and microwave until very soft and pliable, about a minute.
Place a small amount of the chicken mixture and about a tablespoon of the grated cheese down the center of each tortilla. Fold over the edges and arrange them seam-side down in a 9-by-13-inch baking dish. Pour the sauce over the top. Sprinkle the top with the remaining 1 cup grated cheese and bake until bubbly, 20 to 25 minutes.
Serve with a dollop of sour cream and salsa on top and a sprinkle of cilantro leaves.