First, we're going to slightly flatten this chicken (also called 'butterflying' or 'spatchcocking') by laying it breast-side down on a cutting board. Using kitchen shears (or a very sharp knife), remove the backbone (which you should freeze, along with the bones you'll get later, for stock!). Then flip the chicken over and flatten it with your hands. Season generously with salt and pepper.
In a large, heavy-bottomed pot, heat the oil on medium-high. Add chicken breast-side down and cook without flipping until browned, 6 to 8 minutes. (You'll want to have your ventilation hood on for this, and can always lower the heat if pot is smoking excessively or chicken starts to burn.) Flip chicken and cook on the other side for 2 minutes. Transfer to a large plate, and set aside.
To the pot you were cooking the chicken in, immediately add the tomatillos, tomatoes, and garlic. Cook, flipping occasionally, until blistered and browned in spots, about 5 minutes.
Add the chopped onion and cook for a couple of minutes, until softened. Add oregano and bay leaves and cook, stirring, until aromatic, about 30 seconds. Add vinegar and stock. Return chicken to pot, bring to a boil over high heat, then reduce to the mildest of simmers. Cover the pot and cook, turning chicken occasionally, until chicken registers 145°F when an instant-read thermometer is inserted into the center of the thickest part, 18-25 minutes.
Once it's cooked, transfer the chicken to a bowl and set aside.
Continue cooking the sauce at a hard simmer, stirring, for another 5 minutes or so, until it's reduced in volume by roughly half.
Add chipotle chilies and adobo sauce, remove and discard bay leaves, and blend the sauce using an immersion blender or by transferring to a countertop blender -- and be careful, it's hot! Sauce should be relatively smooth. If it seems to be a thinner than you'd like, continue cooking it down at a hard simmer, stirring often, until it reaches your desired consistency.
When chicken is cool enough to handle, separate the meat from the the skin and bones (the latter of which you should freeze for stock!), and finely shred the meat with a couple of forks or your hands. Return the shredded chicken to the sauce. Add fish sauce and stir to combine.
Bring to a simmer for a couple more minutes, until the chicken is coated in sauce, and heated through. Season to taste with salt and pepper (if necessary).
Serve with tortillas, on top of nachos, or just about anywhere you'd use saucy, shredded chicken. Garnish as you like (suggestions in the ingredients above).
Keeps for up to 3 days in a sealed container in the fridge.