Sauté sliced white onion and garlic in the same pot until soft, 4 minutes. Add crushed tomatoes, chipotles with adobo sauce, and oregano; simmer 10 minutes.

Return chicken to the pot, cover, and braise over low heat for 25 minutes until fall-apart tender. Shred the meat and stir back into the sauce; simmer uncovered 5 minutes to thicken.

Char tortillas directly over a gas flame or in a dry skillet. Fill with tinga, pickled red onion, and crumbled queso fresco.