1. FOR THE TINGA: 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 1/2-inch pieces (see Step by Step below); set aside.

2. Heat olive 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, chipotle powder, reserved pork cooking liquid, 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. TO FRY TOSTADAS: Heat vegetable oil in 8-inch heavy-bottomed skillet over medium heat to 350°F. Using fork, poke center of each tortilla 3 or 4 times (to prevent puffing and allow for even cooking). Fry 1 at a time, holding metal potato masher in upright position on top of tortilla to keep it submerged (see photo below), 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.

5. TO SERVE: Spoon small amount of shredded pork onto center of each tostada and serve, passing garnishes separately.

Serves 4 to 6