Veggie Burgers with Mushrooms

Name: Veggie Burgers with Mushrooms
Ingredients: 1 15-ounce can kidney beans, drained and rinsed; 1 small red onion, shredded and squeezed dry (about 1/2 cup); 1/3 cup chopped walnuts; 1 small carrot, finely diced; 1 cup plain or whole-wheat breadcrumbs; 2 scallions, white and green parts, finely chopped; 2 tablespoons chopped fresh parsley; 2 teaspoons Worcestershire or soy sauce; Kosher salt and freshly ground pepper; 3 tablespoons extra-virgin olive oil; 3 cups assorted mushrooms, sliced; 4 English muffins, split and toasted; Mayonnaise and/or mustard, for garnish; Baby spinach or arugula, for garnish