In the bowl of a food processor, pulse sandwich bread to form breadcrumbs. Pour into a bowl and set aside.
Heat 1 tablespoon olive or canola oil in a large skillet set over medium heat. Add onion and sauté until soft. Add garlic, jalapeno, and cumin. Saute for additional 2 minutes.
Scrape the mixture into the food processor. Add black beans, brown rice, lime juice, salt, and pepper. Pulse until the beans are chopped, but not pureed.
Scrape the black bean mixture into a large bowl. Add half of the breadcrumbs and the chopped cilantro. Stir the mixture until combined.
Divide the mixture into 8 equal portions and form into patties. If the mixture is too moist to form patties, add more breadcrumbs.
Place the patties on a baking sheet lined with plastic wrap and cover with additional plastic wrap. Refrigerate for at least ½ hour.
Heat 1 tablespoon canola oil in a large skillet (preferably not nonstick, so a good crust can form) set over medium heat. Add 4 patties and cook for 4 minutes per side. Repeat with 1 tablespoon oil and remaining 4 patties.
Serve 2 patties on each plate, topped with salsa.