Chicken & Mushroom Quesadillas

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1 large boneless, skinless chicken breast (about 8 ounces)

Kosher salt and freshly ground black pepper

4 tablespoons vegetable oil or lard

3 tablespoons unsalted butter

5 ounces white mushrooms, sliced (about 3 cups)

1/2 teaspoon ground cumin

1/2 medium onion, finely chopped

3 cloves garlic, minced

1/2 pickled jalapeno, minced, plus 1 tablespoon pickling juice

1 19-ounce can black beans, rinsed and drained

2 8-inch flour tortillas

2 cups grated white Cheddar cheese (about 8 ounces)

Guacamole and Salsa, for serving, optional