In a food processor, combine the dried porcini mushrooms and fresh thyme. Process until the mushrooms are finely ground. Transfer the porcini mixture to a shallow dish and set aside.

In a mixing bowl, combine the softened butter, finely chopped shallots, balsamic vinegar, and minced garlic. Mix until well combined. Season with salt and pepper to taste. Transfer the mixture to a piece of plastic wrap and shape it into a log. Wrap tightly and refrigerate until firm, about 30 minutes.

Preheat your grill or grill pan over medium-high heat. Pat the T-bone steaks dry with paper towels. Rub each steak with 2 tablespoons of olive oil and season generously with salt and pepper.

Press one side of each steak into the porcini-thyme mixture, ensuring an even coating.

Place the steaks on the grill, coated side down. Grill for about 4-5 minutes, then flip and grill for an additional 4-5 minutes for medium-rare, or until your desired doneness is reached. Remove the steaks from the grill and let them rest for 5-10 minutes to allow the juices to redistribute.

Slice the compound butter into rounds and place on top of the warm T-bone steaks. Garnish with fresh thyme sprigs if desired. Serve with your choice of sides.