Smash the beans in a bowl with a potato masher or fork until slightly chunky. Add the onion, walnuts, carrot, 1/2 cup breadcrumbs, scallions, parsley and 1 teaspoon Worcestershire sauce. Season with salt and pepper and mix with your hands until combined.
Spread the remaining 1/2 cup breadcrumbs on a plate. Form the bean mixture into 4 patties; lightly coat with the breadcrumbs, shaking off any excess. Heat 2 tablespoons olive oil in a large nonstick skillet over medium-high heat. Add the patties and cook until golden and slightly crisp, 2 to 3 minutes per side. Transfer the burgers to a plate.
Heat the remaining 1 tablespoon oil in the same skillet over medium heat. Add the mushrooms and the remaining 1 teaspoon Worcestershire sauce; season with salt and pepper and cook until the mushrooms are slightly wilted, 3 to 4 minutes. Serve the burgers on the English muffins with mayonnaise and/or mustard, baby greens and mushrooms.
Photograph by Antonis Achilleos
Courtesy of Food Network Magazine