Remove and discard the stems and seeds from the ancho and guajillo chiles. Tear the chiles into medium-sized pieces.

Heat a large skillet over medium heat. Add the chiles and toast until fragrant, stirring frequently for about 1-2 minutes.

Transfer the chiles to a medium pot. Add the bay leaf and fill the pot with water until the chiles are completely covered.

Bring the water to a boil over high heat, then remove from heat, cover, and let the chiles soak for 10 minutes.

Transfer the soaked and softened chiles and the bay leaf to a large blender using a slotted spoon.

Add 3 cups of the chile-soaked water, garlic, vinegar, soy sauce, oregano, thyme, sugar, cumin, and salt. Blend until smooth and set aside.

Heat 1 tablespoon of oil in a large pot or Dutch oven over medium-high heat. Add ½ of the pork shoulder and sear on all sides until browned, then transfer to a bowl or large plate.

Add another tablespoon of oil to the pot as well as the remaining pork. Sear on all sides until browned, then transfer to the same bowl or plate.

Add the remaining 1 tablespoon of oil to the pot and add the onion. Cook for 5 minutes, scraping any brown bits that have stuck to the bottom of the pan.

Add the seared pork back into the pot and pour the blended chile sauce on top. Mix together to combine.

Bring the pot to a boil, reduce heat to low, cover, and cook for 2 hours.

Serve in a bowl garnished with chopped cilantro, lime wedges, and a side of warm flour tortillas and/or rice.