Squeeze grated sweet potato with paper towels to remove excess moisture; place in a large bowl. Pulse oats in a food processor until finely ground; add to the bowl with the sweet potatoes. Add beans, scallions, mayonnaise, tomato paste, curry powder and salt to the bowl; mash the mixture together with your hands. Shape into four 1/2-inch-thick patties. Place the patties on a plate; refrigerate for 30 minutes.
Step 2
Stir yogurt, dill and lemon juice together in a small bowl; set aside.
Step 3
Heat oil in a large cast-iron skillet over medium-high heat. Add the patties; cook until golden brown, about 3 minutes per side.
Step 4
Divide the yogurt sauce evenly among top and bottom bun halves. Top each bottom bun half with a burger and cucumber slices; replace top bun halves.