Place a baking sheet on the bottom rack of the oven and preheat to 425 degrees F.
Combine the kale and beans in a medium bowl and mash until the beans almost form a paste. Add the cheese, peanuts, 2 tablespoons of the cornmeal, 1/2 teaspoon salt, some pepper and the egg white. Form into four patties about 1/2-inch thick. Refrigerate for at least 20 minutes. (Can be made ahead and refrigerated overnight.)
Toss the sweet potatoes with 1 tablespoon of the oil and the curry powder. Arrange in a single layer on the preheated baking sheet and bake until soft and golden in some spots, tossing about halfway through, 18 to 20 minutes.
Meanwhile, heat the remaining 1 1/2 tablespoons oil in a large ovenproof nonstick skillet over medium heat. Put the remaining 3 tablespoons cornmeal onto a plate. Dredge both sides of the burgers in the cornmeal. Cook until golden brown, 3 to 4 minutes per side. Transfer the skillet to the oven and bake until the burgers reach an internal temperature of 165 degrees F, about 5 minutes.
Spread each burger with 1/2 tablespoon of the mayonnaise. Build the burgers on the English muffins with lettuce, tomatoes and onions if desired. Divide among four dinner plates along with the sweet potatoes. Divide the yoghurt and peaches among four small bowls and serve on the side.