First, prepare the chicken. Bring a large pot of water to a boil and slice chicken breast into pieces that are roughly the size of your palm. Boil until cooked through, about 10 to 12 minutes. Drain and shred chicken, then set aside.
In the meantime, prepare the rice. Bring 2 cups of water to a boil in a small saucepan, then stir in the rice. Cover and turn heat to low and steam until all the water has been absorbed and rice is fluffy, about 25 minutes.
Preheat oven to 350 degrees F. Add beans, onion, jalapeno, green chiles, shredded chicken, and cooked brown rice to a 9x13 baking dish and stir to combine.
Add lime juice, 1 cup of the enchilada sauce, and 1 cup of the shredded cheese to the casserole dish. Stir gently to combine, then flatten into the dish and smooth the top of the casserole with the back of a spoon.
Rip each tortilla into 8 equal triangles, then lay them in a single layer to cover the top of the casserole.
Top the casserole with the remaining 1 cup of enchilada sauce, spreading it out evenly. Sprinkle with the remaining 1 cup of shredded cheese.
Bake, uncovered, until the cheese is golden-brown and bubbly, about 30 minutes.
Optionally garnish with chopped fresh cilantro, then serve immediately.