Heat your grill to 350°F. While it preheats, pat the chicken breasts dry and coat them evenly with 3 tablespoons of olive oil, then rub generously with 1/3 cup of green chile rub, making sure to coat all sides. Once the grill is hot, place the chicken on the grates and cook for about 5 minutes without moving it—this creates a nice sear. Flip the chicken and continue cooking until the internal temperature reaches 160°F, about another 5-10 minutes depending on thickness. Remove from heat and let rest for 5 minutes before chopping into bite-sized pieces.

In a skillet over medium heat, combine 3 tablespoons of olive oil with 3 tablespoons of all-purpose flour, stirring constantly for about 2 minutes to create a roux base—this will thicken your sauce and give it body. Add the red chili powder, green chile powder, onion powder, garlic powder, cumin, dried oregano, smoked paprika, and salt, stirring well to bloom the spices for about 30 seconds. Pour in the chicken broth and tomato sauce, whisking to combine and break up any lumps, then simmer for 5 minutes. Remove from heat and stir in the heavy cream, tasting and adjusting seasonings as needed. I like to add a pinch more salt here if the sauce tastes flat, as it really brings out the chile flavors.

In a large bowl, combine the softened cream cheese, 3 1/2 cups of shredded cheddar cheese, 2 tablespoons of green chile rub, and the chopped grilled chicken from Step 1, mixing until well incorporated. Working with one tortilla at a time, dip it into the warm enchilada sauce from Step 2, coating both sides lightly, then place on a work surface. Spoon about 1/4 cup of the chicken filling onto the lower third of the tortilla, roll it tightly, and place seam-side down in a 9x13-inch baking dish. I find that dipping the tortillas gently in the sauce keeps them pliable without making them soggy—if your sauce is too thick, thin it with a splash of broth. Repeat with remaining tortillas and filling until the dish is full, arranging the enchiladas snugly in a single layer.

Pour the remaining enchilada sauce from Step 2 evenly over all the rolled enchiladas, making sure each one is covered. Cover the baking dish tightly with aluminum foil and place it on the grill at 350-375°F for about 30 minutes, until the filling is heated through and the edges are bubbling. Remove the foil and sprinkle the top evenly with the reserved cheddar cheese, then return to the grill uncovered for another 10-15 minutes until the cheese is melted and lightly golden. Remove from the grill and let cool for 5 minutes so the filling sets and won't be too runny when you plate.

While the enchiladas are cooling, prepare your fresh toppings: combine the diced tomatoes, finely diced onion, and fresh cilantro in a bowl, squeeze the lime juice over it, and season with a pinch of salt. Arrange the shredded lettuce on serving plates and top with an enchilada or two. Drizzle each plate with salsa and a dollop of sour cream, then finish with a generous spoonful of the fresh tomato-cilantro mixture. Serve immediately while the enchiladas are still warm.