Spicy Mexican Shredded Pork (Tinga) Tostadas

1. FOR THE TINGA: Bring pork, quartered onion, smashed garlic, thyme sprigs, 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, 1-1⁄4 to 1-1⁄2 hours. Drain pork, reserving 1 cup cooking liquid. Discard onion, garlic, and thyme sprigs. Return pork to saucepan and, using potato masher, mash until shredded into rough 1⁄2-inch pieces; set aside. (Pork can be prepared through step 1 and refrigerated for 2 days.)
2. Heat oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add shredded pork, chopped onion, and oregano; cook, stirring often, until pork is well browned and crisp, 7 to 10 minutes. Add minced garlic and cook until fragrant, about 30 seconds.
3. Stir in tomato sauce, reserved pork cooking liquid, chipotle powder, and bay leaves; simmer until almost all liquid has evaporated, 5 to 7 minutes. Remove and discard bay leaves and season with salt to taste.
4. FOR THE TOSTADAS: Heat oil in 8-inch skillet over medium heat to 350 degrees. Using fork, poke center of each tortilla 3 or 4 times. Fry one at a time, holding metal potato masher in upright position on top of tortilla to keep it submerged, until crisp and lightly browned, 45 to 60 seconds (no flipping is necessary). Drain on paper towel–lined plate and season with salt to taste. Repeat with remaining tortillas. (Tostadas can be made up to 1 day in advance and stored in airtight container.)
5. TO SERVE: Spoon small amount of shredded pork onto center of each tostada and serve, passing garnishes separately.

SPICY MEXICAN SHREDDED PORK TOSTADAS WITH HOMEMADE CHORIZO

SERVES 6 TO 8
Increase amount of pork to 3 pounds (2-1⁄2 pounds after trimming). Using two-thirds of pork (1-1⁄2 pounds), follow recipe as directed in step 1. To make chorizo, place remaining pork pieces on large plate in single layer and freeze until firm but still pliable, about 15 minutes. Once firm, toss pork with 1 tablespoon red wine vinegar, 1-1⁄4 teaspoons chili powder, 1 small minced garlic clove, 1 teaspoon salt, 3⁄4 teaspoon hot paprika, 3⁄4 teaspoon ground chipotle powder, 3⁄4 teaspoon dried oregano, 1⁄4 teaspoon pepper, and 1⁄8 teaspoon ground cumin in medium bowl. Pulse half of chorizo mixture in food processor until meat is finely chopped, 8 to 10 pulses. Transfer to bowl and repeat with remaining chorizo mixture. In step 2, heat oil as directed and add chorizo mixture; cook, stirring occasionally, until slightly crisp and no longer pink, 3 to 5 minutes. Transfer meat to paper towel–lined plate, leaving rendered fat in skillet. Proceed with recipe as directed, using rendered fat to cook shredded pork and returning chorizo mixture to skillet along with tomato sauce in step 3.