Preheat the oven to 400 degrees F. Line 2 baking sheets with parchment paper.
In a large bowl, mix together the beans, cheese and chicken. Working in batches, lay out the empanada wrappers on a clean work surface. Place a heaping tablespoon of the bean filling into the center of each wrapper. Fold the dough over the filling to form a half-moon shape and press the edge to seal. Using a fork, crimp the edge to completely seal. Transfer the empanadas to the prepared baking sheets.
In a small bowl, whisk the egg with 2 tablespoons water. Brush the empanadas with the egg wash. Bake until golden brown, 15 to 20 minutes.
To deep-fry the empanadas, heat 1 quart canola oil in a medium pot to 350 degrees F. Assemble the empanadas as above, but leave out the egg wash step. Fry the empanadas in batches until golden brown, 3 to 4 minutes.