Peel one white onion then cut into quarters.
Place whole chicken in a 6 or 8-quart stockpot with onion quarters, 3 whole cloves of garlic, and kosher salt. Cover with cool filtered water by 1-inch. Bring to a simmer for 1 hour, check for doneness.
Meanwhile, dice the remaining onion and garlic; keep them separated. Seed and dice the serrano or jalapeno peppers. Set aside
Strain chicken into a colander set in a large bowl save chicken broth. Do not discard.
Discard onions, garlic, skin, and bones.
Using folks pull the chicken apart to shred or use a hand or stand mixer on low. You can also allow the chicken to cool and shred by hand.
In a large sauté pan over medium-high heat, add to 2 tablespoons of oil. Once hot, add onions and chiles, sauté for 5 to 7 minutes. Add garlic, stirring constantly until fragrant, about 30 seconds to 1 minute.
Add cumin, dried oregano, and dried chiles, sauté for another minute. Add shredded chicken and tomato sauce. Add ¼ to ½ cup of leftover chicken broth if more liquid is needed.
Simmer for 20 minutes over medium-low heat. The chicken should be “saucy” with no runny liquid.