Heat broiler. In a small skillet over medium heat, warm 1 tablespoon olive oil. Cook scallions until softened, 1 minute. Add garlic, jalapeno, and cumin; cook until fragrant, 30 seconds. Transfer to a large bowl.
Add beans to bowl; mash with a fork or a potato masher, leaving about 1/4 of the beans whole. Season generously with salt and pepper. Fold in sweet potato, egg, and breadcrumbs. Divide into 8 balls of equal size; flatten into patties.
Brush a baking sheet with remaining tablespoon oil; place patties on sheet, 1/2 inch apart. Broil 4 inches from heat until golden brown, 8 to 10 minutes. With a thin metal spatula, carefully turn cakes. Broil until crisp, 2 to 3 minutes more. Serve with Lime Sour Cream.
For the Lime Sour Cream: In a small bowl, combine 1/2 cup reduced-fat sour cream with 2 teaspoons fresh lime juice and 1 small minced jalapeno chile (ribs and seeds removed for less heat, if desired) season with coarse salt.
To grate the potatoes with a box grater (instead of food processor), use the large holes and work over a bowl.