Special equipment: Twelve 12-inch metal skewers
Prepare a grill or grill pan for medium-high heat.
Stir together the adobo sauce, 1/2 cup of the ketchup, 2 tablespoons of the Worcestershire sauce and half the lemon juice; set aside.
Gently mix together the ground beef, egg, breadcrumbs, onions, the remaining 2 tablespoons ketchup and 1 tablespoon Worcestershire sauce, 3/4 teaspoon salt and 1/4 teaspoon pepper in a large bowl. Divide into 8 equal portions. Take 1 portion in the cup of your hand. Wrap and shape the meat around a skewer to form a 5-inch log of even thickness, centered on the skewer. Repeat with the remaining 7 portions of meat. Refrigerate the kebabs to let them firm up a little, about 15 minutes.
Meanwhile, place the potatoes in a microwave-safe bowl, and cover tightly with plastic wrap; make a small slit in the center with the tip of a paring knife to vent excess steam. Microwave on high (at 100 percent power) until the potatoes are cooked through, about 7 minutes in a 1,100-watt oven. Let the potatoes cool for a few minutes, then toss with the oil, 1/2 teaspoon salt and a few grinds of pepper. Thread them, cut-sides facing out, on the remaining 4 skewers; reserve the bowl.
Cook the potatoes on the grill until you see grill marks and charring in places, about 2 minutes per side. Slide the potatoes off the skewers back into the bowl. Toss with the remaining lemon juice and the scallions. Add more oil if the potatoes look too dry.
Brush the 8 kebab skewers with oil, and place them on the grill. Cook for 2 minutes on one side, then flip. Brush some of the ketchup glaze on the grilled side. After 2 minutes, flip the skewers again. Continue brushing and flipping every minute or so until the meat is no longer pink inside and is cooked through, 4 to 6 minutes total. Divide the skewers and potato salad among 4 plates, and serve.