For the burgers:
1 large egg, lightly beaten
2 (15.5-ounce) cans low-sodium black beans, drained and rinsed
1/3 cup dry bread crumbs
1/4 cup finely chopped red onion
1/4 cup chopped cilantro
3 tablespoons canola mayonnaise
1 teaspoon ground cumin
For the chipotle ketchup:
1/2 cup ketchup
1/2 chipotle in adobo, minced (about 1 tablespoon), or to taste
1 teaspoon lime juice
1 teaspoon honey
1/4 teaspoon chili powder
To make the burgers:
2 tablespoons olive oil
4 Hawaiian sweet hamburger rolls, split and toasted
Make the bean burger patties: Combine the egg and beans in a large bowl and mash them into chunks with a potato masher or large fork. (All the beans should be broken up, but there should still be pieces visible.) Add the breadcrumbs, onion, cilantro, mayonnaise, and cumin; stir to thoroughly combine. Form into four 1/2-inch-thick patties.
Make the ketchup: Combine the ketchup, chipotle, lime juice, honey, cumin, and chili powder in a bowl, and set aside.
Cook the burgers: Heat the oil in a large nonstick skillet over medium-high. Add the patties and cook until crisp and heated through, about 4 minutes per side. Serve on the rolls topped with the chipotle ketchup.