In a small skillet, heat 2 tablespoons of canola oil over medium-high heat. Fry the tortillas for no longer than 20 seconds, just to soften. Place the tortillas on a large towel or stack of paper towels to drain.
Heat the remaining 1 tablespoon of canola oil in separate skillet over medium heat. Add the onion and jalapeño, and sauté for 1 minute, just to start the cooking process. Add the chicken, half of the green chiles, and 1/2 teaspoon of the paprika. Stir together. Add 1/2 cup of the chicken broth and stir. Add the heavy cream and stir, allowing the mixture to bubble and get hot. Turn off the heat and set aside.
In a separate large skillet, melt the butter and sprinkle in the flour. Whisk together and cook over medium heat for 1 minute. Pour in the remaining 1 1/2 cups of chicken broth. Whisk together and cook until it begins to bubble, 1 to 2 minutes more. Stir in the remaining half of the chiles. Reduce the heat, then stir in the sour cream. Add 1 1/2 cups of cheese and stir to melt. Add the remaining 1/2 teaspoon of paprika. Check the seasonings and add salt and pepper as needed.
Preheat the oven to 350°F.
To assemble, spoon the chicken mixture on top of the tortillas, one by one. Top with plenty of cheese and roll up. Place seam side down in a 13-by-9-inch casserole dish.
Pour the cheese mixture all over the top of the tortillas. Top with extra cheese if you’d like, then bake for 30 minutes. Sprinkle generously with chopped cilantro.
