Roast the chiles over the open flame of a gas burner by holding them with tongs and turning them in the flames until the skins are blistered all over.
Place the roasted chiles in a paper bag and roll the top of the bag to seal it. Allow the chiles to rest in the bag for 15 minutes to steam.
Gently rub the chiles to remove the skins. Remove the seeds from the chiles and dice the flesh.
Heat the oil in a skillet over medium heat. Add the onion and cook, stirring frequently, until the onion is soft, about 8 minutes.
Add the butter and stir until the butter melts. Add the mushrooms and continue cooking until the mushrooms are soft and cooked through, about 8 more minutes. Season to taste with salt and pepper.
Transfer the onion and mushroom mixture to a medium mixing bowl and add the diced chiles. Stir to combine.
Preheat the oven to 350 degrees.
Remove any excess fat and silver skin from the pork loins. Butterfly a pork loin by cutting it lengthwise, being careful not to cut all the way through.
Spread the loin open and cover with plastic wrap. Using a meat mallet, pound the pork loin to an even thickness of about 1/2 inch.
Spread half of the chile mixture over the first pork loin.
Roll the loin tightly lengthwise. If desired, tie the loin with butcher's twine. Repeat the process with the remaining loin and chile mixture.
Sprinkle the loins generously with salt and pepper and 1/2 teaspoon of cumin on each loin.
Heat an ovenproof skillet over high heat. Add the pork loins seam-side down. Cook for 2 minutes before turning. Cook each side for 2 minutes to achieve a nice brown sear on all sides. Remove the skillet from the heat and add the beer.
Transfer the skillet to the oven and cook for 20 minutes.
Allow the pork loins to rest for 5 minutes before slicing and serving.