Step 1

Melt butter in large skillet over medium heat. Roughly chop 1 jalapeno pepper and 1 poblano pepper; add to the skillet with chicken and garlic. Squeeze lime over mixture and add lime rind to the skillet. Cook, covered, until chicken is no longer pink and juices run clear, stirring occasionally, 20 to 25 minutes. Remove from heat and let cool.

Step 2

Meanwhile, set an oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil. Place remaining jalapeno and poblano peppers onto the prepared baking sheet.

Step 3

Cook peppers under the preheated broiler until the skin of the peppers has blackened and blistered, 5 to 8 minutes. Lower oven temperature to 375 degrees F (190 degrees C).

Step 4

Chop cooked chicken into small pieces and place into a bowl. Add hot peppers to the bowl, cover, and let steam for 10 minutes. Peel skin from peppers, remove seeds, and slice.

Step 5

Place small amount of enchilada sauce on the bottom of a 9x13-inch pan, just enough to cover the bottom. Place 5 tortillas on on top. Place 1/2 of the sliced poblano and jalapeno peppers on top of tortillas. Lay out 1/2 of the chicken and 1/2 of the Mexican cheese on top of the peppers. Spoon 1/2 of the remaining enchilada sauce on top of cheese layer. Repeat layering steps. Top with chopped cilantro.

Step 6

Bake in the preheated oven until cheesy is melted and browning, about 25 minutes.