Bring a medium pot of water to a boil. Add kamut, reduce heat to medium-low, cover and simmer until tender, about 1 1/2 hours; drain well and set aside to cool. Meanwhile, put potatoes in a small pot, cover with water, and bring to a boil. Reduce heat to medium-low and simmer until almost tender, 8 to 10 minutes. Drain well, cool, peel, and grate.
Heat 2 tablespoons oil in a large skillet over medium-high heat. Add yellow onions, carrots, chilies, and leeks and cook, stirring occasionally, until softened, 8 to 10 minutes. Add palm fronds and garlic and cook 2 to 3 minutes more; set aside to cool. Meanwhile, pulse 1 cup beans in a food processor until smooth.
In a large bowl, using a spoon or your hands, mix together kamut, potato, onion-carrot mixture, mashed beans, remaining 1 cup whole beans, bread crumbs, flaxseeds, chives, parsley, mustard, marjoram, vinegar, hot sauce (if using), zucchini, salt, and pepper until combined. Form mixture into 18 (3-inch) patties, using about 1/3 cup mixture to make each. Transfer to a sheet tray when done; set aside.
Heat 2 tablespoons oil in a large skillet over medium-high heat. Add red onions and cook, stirring often, until golden brown, about 7 to 8 minutes. Add plum paste, agave nectar, vinegar, and pepper flakes. Reduce heat to medium-low and cook until soft and fragrant, 3 to 4 minutes more; set aside.
Heat 1 1/2 tablespoons oil in a large skillet over medium heat. Arrange half of the patties in skillet and cook, flipping once, until golden brown and hot throughout, 8 to 10 minutes total; transfer to a plate when done and keep warm. Repeat process with remaining 1 1/2 tablespoons oil and patties. Spread mustard on focaccia or rolls, if you like, and then top with patties, red onion mixture, and sprouts. Serve immediately.