1. Heat grill to medium-high. Allow steak to come to room temperature; season with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper. Grill steak 4 to 5 minutes per side, or until the internal temperature reaches 135 degrees for medium-rare. Set aside to rest for 10 minutes.
2. Meanwhile, combine vinegar and shallots in a medium saucepan set over medium heat. Bring to a simmer and reduce liquid by half, about 5 minutes. Stir in blackberries, thyme, honey and 1 tablespoon water. Bring to a simmer and cook until berries burst and sauce thickens, about 10 minutes.
3. Slice meat thinly against the grain. Pour any accumulated drippings into sauce. Remove sauce from heat and stir in butter to melt. Add 1/4 teaspoon of the salt and remaining 1/8 teaspoon pepper. Sprinkle remaining 1/4 teaspoon salt over sliced meat. Serve with sauce.