Melt the butter in an 8-inch skillet over medium-low heat. Add the garlic, onion powder, pepper and salt. Cook until fragrant, about 1 minute. Transfer all but 1 tablespoon of the butter mixture into a small bowl and let cool slightly, about 5 minutes.
While the butter mixture is cooling, add the tomato paste to the skillet with the remaining butter mixture and cook over medium heat until the paste begins to darken, about 1-2 minutes. Stir in the broth, raisins, soy sauce, mustard, vinegar, and Worcestershire sauce and simmer the mixture until the raisins are plump, about 5 minutes. Transfer the sauce to a blender and process until the mixture is very smooth.
Place the ground sirloin in a large bowl. Add 5 tablespoons of the reserved and cooled butter mixture and the soy sauce and knead until well combined. Shape the meat into 8 patties, about 3/4-inch thick and press a shallow divot in the center. Brush each patty all over with a tablespoon or so of the simmered steak sauce.
Combine the remaining 2 tablespoons of the cooled butter mixture with 2 tablespoons steak sauce and set aside.
To grill, turn all burners of a gas grill to high, cover and heat the grill until hot, about 15 minutes. Leave the burners on high. Clean and oil the cooking grate. Grill the burgers, covered, for about 5-6 minutes per side (for medium-well). Transfer the burgers to a plate, tent with foil and let them rest for about 5-10 minutes. Meanwhile, brush each cut side of the potato rolls with the reserved butter-steak sauce mixture. Grill the buns, cut side down, until golden, about 2 minutes. Place burgers on the buns and serve with remaining steak sauce.
Recipe adapted from www.melskitchencafe.com.