Set broiler to high heat. Place chilies on a baking sheet and roast until blackened, 10-12 minutes, turning once halfway through cooking time. Place in a zip top bag and allow to cool.

Meanwhile, cook spaghetti according to package directions until just al dente. Preheat oven to 375 degrees.

In a large skillet over medium heat, melt butter. Add onion and garlic and cook until soft, about 5 minutes. Stir in flour and cook 1-2 minutes more.

Whisk in half-and-half and broth. Cook and stir until sauce is thickened, about 5 minutes. Reduce heat to low. Stir in half of the Monterey Jack and half of the Pepper Jack cheese.

Stir in cilantro, cumin salt and pepper and red pepper flakes and lime juice. Remove chilies from bag and rub off skin. Remove stems and seeds and dice. Add to skillet, along with the chicken. Add spaghetti and stir to coat well.

To with remaining cheese. Bake for 25-30 minutes, until light brown and bubbly. Garnish with fresh cilantro or pico de gallo, if desired.