Heat the oven to 400°F and coat a 10-inch oven-safe skillet with the vegetable oil.
Bring the broth to a boil, whisk in the polenta and 1/2 teaspoon salt and cook until very thick, 5 to 7 minutes.
Stir the butter into the polenta, spread it in the skillet and refrigerate it for 15 minutes.
Mix the cooked chicken, black beans, enchilada sauce, chipotle, cumin and remaining salt and spread the filling over the polenta.
Top the pie with pepper Jack cheese.
Bake until the filling bubbles and the cheese browns, 20 to 25 minutes.
Rest the pie for 10 minutes before cutting it into wedges.