In a bowl, combine 3 tablespoons softened butter and 2 tablespoons chopped fresh basil; season with salt and pepper; refrigerate. Preheat a grill to medium-high. In a large bowl, combine 1/4 cup brown sugar, 2 tablespoons each sweet smoked paprika, garlic powder and extra-virgin olive oil, 1 tablespoon each chili powder, dried basil and dried thyme and 2 teaspoons dry mustard. Add 1 1/2 pounds flank steak, cut against the grain into 16 slices, and 16 cherry tomatoes; season with salt and pepper and toss to coat. Thread 2 pieces of steak, ribbon-style, and 2 tomatoes onto each of eight 12-inch skewers. Cover and grill, turning once, until the steak is just cooked through, about 7 minutes. Top with the basil butter.