Grilled Flank Steak with Chimichurri Sauce

Combine 2/3 cup oil, 5 cloves garlic,1 tablespoon balsamic vinegar, lemon juice, 2 tablespoons ginger, and soy sauce in a shallow baking dish. Add steak, turning to coat. Cover and refrigerate overnight, turning occasionally. Drain tomatoes, reserving tomatoes and juice separately. Combine remaining 1/3 cup oil, 1 clove garlic, 3 tablespoons balsamic vinegar, 1 1/2 tablespoons ginger, salt, barbecue sauce, and reserved tomato juice in container of an electric blender; cover and process until smooth. Pour into a bowl; add reserved tomatoes. Cover and refrigerate until ready to serve. Place steak on cooking grate; grill over medium-hot coals (350? to 400?) 7 to 8 minutes on each side or to desired degree of doneness. Cut steak diagonally across grain into thin strips; serve with tomato mixture.