Melt 1 tablespoon butter in a small skillet over medium heat. Add the shallots and cook, stirring occasionally, until soft but not browned. Add 2 cloves minced garlic and cook for 30 seconds. Place mixture in a small mixing bowl and let cool. Add the remaining butter, chives, and 1 tablespoon Worcestershire sauce. Mix well. Transfer butter mixture to plastic wrap and form butter into 5-inch-long log. Roll up in plastic, enclosing completely. Refrigerate until firm. (Can be prepared 3 days ahead. Keep refrigerated.)
Combine the remaining ¼ cup Worcestershire sauce, remaining 2 minced garlic cloves, olive oil, tamari, lemon juice, Italian seasoning, black pepper, onion powder, and salt in a mixing bowl and mix well. Pour into a large resealable food storage bag, add the steaks, and marinate in the refrigerator for 1 hour up to 24 hours. Remove the steaks from the marinade, pat dry with paper towels, and let sit at room temperature while the grill heats.
Prepare grill for direct heat and preheat to medium-high. Oil the grates with vegetable oil.
Grill the steaks with the lid closed for 5 minutes per side or until it reaches an internal temperature of 130 degrees for medium rare. Remove from grill and let rest for 5-10 minutes.
Slice the compound butter into 8 slices, top the warm steaks with 2 slices per steak and serve.