Clean and blanch the pig feet: Rinse pig feet under cold running water, place in a large pot, cover with cold water, add 1 tablespoon salt, bring to a boil over high heat and boil for 5 minutes, then drain and rinse under cold water; pat dry with paper towels.

Prepare aromatics and seasonings: Mince 8 cloves garlic and quarter 1 yellow onion, and gather mustard seeds, bay leaves, thyme, and red pepper flakes.

Heat oil and brown pig feet: Heat 2 tablespoons vegetable oil in a Dutch oven over medium-high heat until shimmering, then brown the pig feet 3 to 4 minutes per side without moving to develop a crust, working in batches if needed, and transfer to a plate.

Build the braising liquid: In the same pot, add minced garlic and cook for 30 seconds, then pour in 1 cup apple cider vinegar and 1/2 cup soy sauce, scraping the bottom of the pot. Add 6 cups water or chicken broth, 1 tablespoon sugar, and bay leaves, stirring to combine.

Return pig feet to the pot: Nestle browned pig feet into the braising liquid along with the quartered onion, thyme sprigs, mustard seeds, and red pepper flakes, stirring gently to distribute.

Braise low and slow: Cover the pot and place in a preheated 325°F oven; braise for 2 1/2 to 3 hours, stirring gently at the 1 1/2-hour mark for even cooking.

Check for doneness: Remove the pot and test one pig foot with a fork; meat should pull easily from the bone and reach an internal temperature of 190°F to 200°F. If needed, return to oven for 20 to 30 more minutes.

Strain and finish the sauce: Transfer pig feet to a serving platter and cover with foil. Strain the braising liquid through a colander into the pot, discarding solids, then simmer the liquid over medium heat for 5 to 10 minutes to reduce and thicken.

Serve: Pour the reduced sauce over the pig feet on the platter and serve hot with crusty bread or rice for soaking up the sauce.