Preheat your oven to 350ºF.
Add the mole sauce, chicken broth, and black beans to a large skillet over medium heat. Cook for 3-4 minutes while stirring everything together. Once the sauce has slightly thickened and coats the back of the spoon, turn off the heat. (If you're using mole paste, cook it down with the broth or water on its own until smooth before adding the beans.)
Add the pulled rotisserie chicken and stir to coat the chicken in the sauce.
Transfer half the chicken mixture to a bowl before adding four corn tortillas and half the cheese on top of the remaining half in the skillet.
Add three-fourths of the reserved chicken mixture on top before adding the remaining tortillas. Top the tortillas with the final bit of chicken mole and cheese.
Bake for 25-30 minutes until the sauce is bubbling around the edges and the cheese is golden brown.
Let the chicken casserole rest for 5-10 minutes before slicing and serving. Garnish with cotija cheese, freshly chopped cilantro and white onion, and a squeeze of lime juice, if desired.