Place a rack in middle of oven; preheat to 450°. Place 2 lb. sweet potatoes (about 4 medium or 6 small), scrubbed, cut into ½“-thick wedges, on a foil-lined rimmed baking sheet. Drizzle extra-virgin olive oil over, season with kosher salt, and toss to coat. Spread out sweet potatoes in a single layer on baking sheet and roast, turning halfway through, until tender and browned in spots, 35–40 minutes.
Meanwhile, heat 1 Tbsp. extra-virgin olive oil in a large skillet over medium-high. Cook 1 lb. ground beef, undisturbed, until well browned underneath, about 3 minutes. Add 1½ tsp. ground cumin, 1 tsp. smoked paprika, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt; season generously with freshly ground pepper. Cook, stirring and breaking meat apart into small pieces with a wooden spoon, until beef is just about cooked through, about 2 minutes. Add 4 garlic cloves, thinly sliced, and 2 Tbsp. tomato paste; cook, stirring often, until meat is coated and tomato paste is slightly darkened, about 2 minutes. Add half of 14 oz. Napa cabbage kimchi, coarsely chopped, and cook, stirring, until kimchi is softened, about 1 minute. Pour in ½ cup water; cook, stirring and scraping up any browned bits stuck to bottom of pan, until liquid is thickened and saucy, about 1 minute.
Remove sweet potatoes from oven; heat broiler. Toss sweet potatoes on baking sheet, then spoon beef mixture over. Top with remaining kimchi. Scatter 12 oz. extra-sharp white cheddar, coarsely grated, evenly over. Broil until cheese is melted and blistered in spots, about 4 minutes.
Just before serving, scatter ½ cup sliced pickled jalapeños, coarsely chopped, over; top with thinly sliced scallions and cilantro leaves.