Heat olive oil in a large pot. Add chopped onion and cook until soft and translucent. Add garlic in the last minute or to and let it start to brown.
Place the remaining ingredients up to the chicken broth into the pot. Add enough chicken broth to cover the ingredients. Start with 1 cup and go from there.
Bring to a boil, turn down heat, and simmer, uncovered, for 30 minutes, Chicken should be done. Remove the chicken, let cool slightly, then shred.
Continue to cook the sauce for another 20-30 minutes.
Puree the mixture by either using an immersion blender or placing the mixture in batches in a blender. WARNING: You do not want to fill the blender too full of hot liquid as it could explode. Process in batches.
Place mixture back into the pot and add shredded chicken. Keep cooking until the chicken has warmed through.
Heat your tostadas in a 325°F oven for 3-4 minutes.
Place a tostada on each plate, spread it with some warmed refried beans then ladle chicken tinga on top. Garnish with your favorite toppings.
Notes
STORE/FREEZEStore the cooled chicken tinga in an airtight container in the refrigerator for up to 4 days. Store tostadas separately in their packaging to keep them crispy.Freeze the leftovers in a freezer-safe container for up to 3 months. Let it thaw overnight in the refrigerator before reheating.*Note: Nutrition information and total calories does not include the toppings.