Wash and scrub sweet potatoes, then pierce with a fork. Microwave until fork-tender, 5–8 minutes, rotating halfway. Cut in half lengthwise, let cool slightly, and peel. Coarsely chop to measure 1-1/3 cups and set aside.
Drain and rinse black beans, then set aside to dry. Grate peeled carrots and 1/2 of a large red onion. Measure 3/4 cup of grated carrots and 1/3 cup of grated onion (lightly packed), and set aside.
Pulse cashews in a large food processor until coarsely chopped. Add black beans, red onion, carrot, sweet potato, garlic, cilantro, paprika, cumin, chili powder, garlic powder, salt, and pepper. Pulse 5 times, scrape sides, and pulse 5 more times until well mixed. Add mayo, panko, and Parmesan. Pulse 10 times, stirring in between. Add cooked rice. Blend and pulse 3 times, scrape edges, and pulse 3 more times, just to incorporate rice. See note 5 for troubleshooting.
Pack the mixture into a 1/2-cup measuring cup and place on a parchment or foil-lined sheet pan, making 9 mounds. Distribute any remaining mixture evenly. Spritz your hands with cooking spray, shape each mound into a 3/4-inch thick, 4-inch wide patty. Freeze patties 20–30 minutes.
Heat 2 tablespoons oil over medium-high. Add 3 patties from the freezer and cook until golden and crispy, 3–4 minutes per side. Transfer to a plate and repeat with the remaining patties. Avoid crowding the pan.
Toast buns (see note 6). Spread mayo on the bottom bun, then layer with lettuce, veggie patty, avocado, tomato, and onion. Add mayo to the top bun, assemble, and enjoy.
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Notes
Note 1: You’ll need 1 extra-large potato, 2 medium, or 3 small. Measure to get 1-1/3 cup cooked and diced sweet potatoes for this recipe.Note 2: Parmesan from a can will be too salty and overpowering in these patties. Use the freshly grated, sandy-like consistency.Note 3: Any cooked and leftover rice will work. To keep things easy, I use this packaged rice blend and microwave it for 1 minute. One container is the perfect amount here!Note 4: For serving: 9 buns (I love Brioche best!) and softened butter, mayo, green leaf lettuce, ripe (soft) avocado or guacamole, tomato, red onion, cheese slices. I love ripe avocado on these burgers. If unavailable, use Hass avocado minis instead. For cheese, add a slice when flipping the patty and cover the pan to melt.Note 5: Trouble-shooting: Mixture falling apart? Pulse longer. Too wet? Add a bit more panko.Note 6: Toast the buns: To prevent soggy buns, spread softened butter on the insides and toast them, butter side down, on a medium heat pan or grill for 30 seconds to 1 minute until golden. Remove from heat. Subsequent batches toast faster as the pan heats up.Nutrition Note: Nutrition information is for the burger only since buns and toppings will vary according to preference.Storage: Since you freeze the burger patties before cooking, it’s also the perfect opportunity to store some for later! Tightly wrap individual frozen patties, then add them to a large freezer bag.