2 tablespoons olive oil, divided
1/2 medium onion, diced
2 cloves garlic, minced
2 (14-ounce) cans white beans, drained and rinsed
1/2 cup breadcrumbs
1/3 cup shredded Parmesan cheese
1/4 cup fresh parsley leaves, coarsely chopped
1 large egg, beaten
3 tablespoons lemon juice
1 tablespoon anchovy paste
2 teaspoons Worcestershire sauce
2 teaspoons Dijon mustard
1/4 teaspoon kosher salt
1/4 teaspoon freshly ground black pepper
4 hamburger buns