Purée all ingredients except steak in a blender until smooth. Trim fat from meat and discard. Cut meat into approximately 1" cubes. Place meat in a large bowl with marinade and toss to coat; cover and chill overnight.
Remove meat from marinade. Thread onto skewers and leave at least 1" of space at the ends of skewers for easy turning. Discard marinade
For the Scallion Dipping Sauce
Combine all ingredients in a large bowl just before you begin grilling; stir occasionally.
For the Basting Sauce
Transfer all ingredients to a small saucepan and cook over medium-low heat until just heated through; keep warm.
Build a medium fire in a charcoal grill, or heat a gas grill to medium-high. Grill skewers, brushing with basting sauce and turning every 2 minutes, for 10 minutes. Stop basting and cook, turning every 2 minutes, until browned around edges and cooked through, about 6 minutes more. Serve with scallion dipping sauce on the side.