Combine the chicken, salsa verde, broth, cumin and salt in a covered skillet and bring it to a gentle simmer.
Cook over medium-low heat for 22 to 28 minutes, turning once, until the thighs reach 165°F.
Transfer the chicken to a bowl, shred it with 2 forks and stir in 1/2 cup of the reduced skillet sauce.
Warm the refried beans in the same skillet for 3 to 4 minutes and toast the bolillo cut sides under the broiler for 1 minute.
Spread each roll with warm beans and add one-fourth of the shredded chicken, 3 avocado slices and 2 tablespoons queso fresco.
Spoon 1 tablespoon thick salsa-verde pan sauce over each filling and close the tortas.