For the butter: In a food processor, combine the butter, scallions, garlic, and soy sauce. Pulse until smooth. Place the mixture on a piece of plastic wrap and form into a log about 1-inch in diameter and 7 inches long. Roll the log in the plastic wrap and refrigerate until firm enough to slice, about 30 minutes. Slice into 1/4-inch pieces.
For the skewers: In a small bowl, mix together the olive oil, garlic, salt, and pepper. Thread 4 pieces of mushroom onto 6 of the skewers. Thread 4 shrimp onto 7 of the skewers. Thread 4 pieces of the steak onto the remaining 7 skewers. Arrange the skewers in a single layer on 2 baking sheets. Spoon the oil mixture over the top and marinate for 15 minutes.
Place a grill pan over medium-high heat or preheat a gas or charcoal grill. Grill the beef skewers for 3 minutes each side for medium-well. Let the meat rest for 5 minutes. Grill the shrimp skewers for 2 minutes each side until opaque and cooked through. Grill the mushroom skewers for 4 minutes each side until tender. Arrange the skewers on a platter and serve with the sliced butter.