In a slow cooker, mix salsa, green chiles, lime juice, chili powder, garlic, and cayenne pepper. Place chicken in the slow cooker and cover with some of the salsa mixture. Cook on HIGH for 3-4 hours, or on LOW for 5-6 hours.
Once chicken is fully cooked, transfer chicken to a bowl where you can shred the chicken, using two forks. Carefully put shredded chicken back in the slow cooker, and mix in with the salsa mixture.
Add black beans and 1/4 cup shredded cheese to the slow cooker and mix well.
Scoop 1/2 cup of the chicken/bean mixture on each tostada shell. Top with 1 tablespoon cheese, a few sliced cherry tomatoes, and approximately 3 tablespoons diced avocado.
IF USING AN INSTANT POT
Put 1 cup water and chicken in an Instant Pot. Cook chicken in Instant Pot for 12 minutes on HIGH pressure and quick release once fully cooked. Mix the salsa, green chiles, lime juice, chili powder, cayenne pepper, black beans, and 1/4 cup mozzarella cheese in with the chicken.
Mix the salsa, green chiles, lime juice, chili powder, garlic, cayenne pepper, black beans, and 1/4 cup mozzarella cheese in with the chicken.
Scoop 1/2 cup of the chicken/bean mixture on each tostada shell. Top with 1 tablespoon cheese, a few sliced cherry tomatoes, and approximately 3 tablespoons diced avocado.
IF USING THE STOVE-TOP
Place chicken breasts into a saucepan and pour in enough water to cover. Place over medium heat, bring to a boil, and simmer until chicken is no longer pink, about 10 to 12 minutes. Transfer chicken breasts to a bowl, allow to cool, and shred the chicken with 2 forks.
Mix the salsa, green chiles, lime juice, chili powder, garlic, cayenne pepper, black beans, and 1/4 cup mozzarella cheese in with the chicken.
Scoop 1/2 cup of the chicken/bean mixture on each tostada shell. Top with 1 tablespoon cheese, a few sliced cherry tomatoes, and approximately 3 tablespoons diced avocado.