Preheat your oven to 375°F (190°C). Warm the corn tortillas briefly in a dry skillet or microwave until soft and pliable; this prevents cracking when rolling.
In a mixing bowl, combine the shredded chicken with a squeeze of lime juice, salt, and pepper for an extra flavor boost. Set aside.
In a saucepan, heat the oil over medium heat; add a pinch of salt and cook the enchilada sauce with heavy cream, smoked paprika, and a splash of lime juice until bubbling and slightly thickened, about 5 minutes. Stir occasionally and taste, adjusting seasoning as needed.
Spread a thin layer of the sauce on the bottom of your baking dish to prevent sticking. Spoon some of the chicken mixture onto a tortilla, sprinkle with shredded cheese, then roll it up tightly to enclose the filling.
Create a layered assembly by placing the rolled tortillas seam-side down in the baking dish, then pour more of the warm sauce evenly over the top. Sprinkle the remaining cheese generously over the surface.
Bake uncovered in the preheated oven for 20-25 minutes, until the cheese is melted, bubbling, and lightly golden around the edges.
Remove from oven and let rest for a few minutes. Garnish with fresh herbs or additional lime wedges if desired, then serve hot, enjoying the gooey cheese and aromatic sauce.