MAKE the Kebabs: In a large plastic resealable bag, combine the beef with smoked paprika and black pepper. Seal bag; toss to coat. Add the vinaigrette; seal bag and toss to coat. Marinate in the refrigerator at least 2 or up to 3 hours.
MEANWHILE, place the Brussels sprouts in a large microwave-safe bowl or dish. Cover and cook on high for 3 minutes to soften. Drizzle with the oil; add the garlic, salt, and ½ teaspoon of the black pepper; toss to coat.
MAKE the Sweet Potato Hash Browns: In a food processor fitted with the chopping blade, combine the jalapeño and scallions. Cover and process until chopped. Change to the shredding blade, and shred potatoes. Transfer potato mixture to a large bowl; drizzle with 3 tablespoons of the oil and season with salt and pepper; toss to combine.
IN a large nonstick or cast-iron skillet heat 1 tablespoon of the oil over medium heat. Working in batches if necessary, drop the sweet potatoes onto the hot skillet in 4 mounds, about 1 1/4 cups each; flatten slightly. Cook until potatoes are crisp and golden brown on the bottom, about 10 minutes. Turn potatoes over, and cook until bottom is golden brown, about 5 minutes more.
MEANWHILE, preheat the grill or a grill pan to medium heat. Remove the beef from the marinade; discard the marinade. Thread the beef and sprouts alternately on metal or wooden* skewers, allowing at least 1/2-inch between pieces. Place kebabs on the grill rack. Grill, turning once halfway through, until cooked to desired doneness, 8 to 10 minutes for medium.
SERVE the kebabs with hash browns.
*If using wooden skewers, soak in water for 30 minutes before using.