Prepare the chicken: In a large pot, add chicken breasts with enough water to cover. Add 1 clove garlic, half an onion, and 1 teaspoon salt. Bring to a boil, then reduce heat and simmer for 20 minutes until chicken is cooked through. Remove chicken and let cool, reserving 1 cup of cooking broth. Shred chicken with two forks and set aside.

Make the tinga sauce: Heat 2 tablespoons vegetable oil in a large skillet over medium heat. Add diced onions and cook until softened, about 5 minutes. Add minced garlic and cook for 1 minute until fragrant.

Blend the sauce: In a blender, combine diced tomatoes, chipotle peppers (from canned chipotles in adobo), 1 cup reserved chicken broth, cumin, oregano, and salt. Blend until smooth.

Combine and simmer: Pour the blended sauce into the skillet with onions. Add shredded chicken and stir to combine. Simmer for 15 minutes, stirring occasionally, until sauce thickens and chicken is well coated. Adjust seasoning with salt and pepper.

Prepare tostadas: If using corn tortillas, heat vegetable oil in a skillet over medium-high heat (about 1/2 inch deep). Fry tortillas one at a time for 30-45 seconds per side until golden and crispy. Drain on paper towels. Alternatively, use pre-made tostada shells or bake tortillas at 400°F for 8-10 minutes until crispy.

Warm the beans: Heat refried beans in a small saucepan over low heat, stirring occasionally, until warmed through.

Assemble tostadas: Spread a layer of warm refried beans on each tostada. Top with a generous portion of chicken tinga. Add shredded lettuce, crumbled queso fresco, and a drizzle of Mexican crema or sour cream.

Serve immediately: Arrange tostadas on a platter and serve right away while still crispy. Offer lime wedges and extra hot sauce on the side for those who want additional heat.