Heat a Dutch oven or a deep skillet over medium heat. Tear the chiles, discarding the stems and add them to the skillet. Toast for 4 minutes, stirring or shifting the chiles every minute. Remove the chiles from the skillet, and transfer to a bowl. Add hot water, just enough to cover, and set aside.
Add 1 tbsp of oil to the pan. Season the chicken thighs on both sides with a pinch of kosher salt. Once hot add the chicken thighs to the pan and sear for 4 minutes on each side. Remove from the pan (they wont be fully cooked through) and place in a bowl for later.
Add another tbsp of oil to the pan and toss in the cut onions. Cook for 2 minutes then toss in the sliced garlic and cook for another 2 minutes.
Stir in the Mexican oregano, paprika, cumin, cinnamon, and thyme. Cook for 1-2 minutes, mixing every few seconds to ensure the spices dont stick and burn. If the pan is dry add another tbsp of oil. Pour in the chicken broth, scraping the bottom of the skillet to release and incorporate the spices. Remove from heat.
To a blender add: the rehydrated chiles + 1/4 cup of the soaking liquid, crushed tomatoes, apple cider vinegar, the onions garlic broth mixture, and 1/2 bunch of cilantro (throughly washed bottom stems discarded). Blend on high for 30 seconds or until smooth.
Return the chicken back to the pan with the juices that pooled on the plate. In 3 batches pour the sauce through a fine mesh strainer, pushing through the sauce until you are left with a thick paste (discard and pour more sauce). Add the bay leaves to the pot.
Bring the pot to a simmer over medium-high heat.Once it reaches a simmer, season with salt to taste, then reduce the heat to low. Cover with the lid and simmer for 45 minutes.
After the 45 minutes test the chicken, if the chicken can easily be pulled apart, remove from the heat and shred the chicken. If not simmer for another 15 minutes before shredding.
Serve the chicken birria over white rice, garnished generously with cilantro, diced white onion, sliced jalapeños, a squeeze of lime, and a healthy amount of birria sauce.