1. Bring pork, quartered onion, smashed garlic cloves, thyme, 1 teaspoon salt, and 6 cups water to simmer in large saucepan over medium-high heat, skimming off any foam that rises to surface. Reduce heat to medium-low, partially cover, and cook until pork is tender, 75 to 90 minutes. Drain pork, reserving 1 cup cooking liquid. Discard onion, garlic, and thyme. Return pork to saucepan and, using potato masher, mash until shredded into rough ½-inch pieces (see Step-by-Step below); set aside.