Veggie Burger

Name: Tex-Mex Veggie Burger
Ingredients: ⅓ cup white long-grain rice; 2 15-ounce cans black beans, rinsed; 1 medium shallot, chopped; 6 slices pickled jalapeño; 1 tablespoon prepared barbecue sauce; 1 teaspoon chili powder, preferably ancho; ½ teaspoon ground cumin; 1 large egg white; Kosher salt, freshly ground pepper; 4 tablespoons vegetable oil, divided; 6 hamburger buns; Favorite burger toppings (for serving)