In a medium saucepan, bring salted water to a boil; add the carrot pieces and cook until easily pierced with a fork. Place carrot in a food processor or blender, and puree; set aside. In the same saucepan, over medium-high heat, place garlic, 1 tablespoon of the butter, and the sherry. Cook and stir occasionally, until reduced by half. Add the pureed carrot to the mixture, and continue to stir constantly for 1 minute. Remove the pan from heat, and whisk in the Worcestershire Sauce. Add the remaining butter, one tablespoon at a time, until all is incorporated and the sauce is smooth. Season to taste with salt and pepper before serving.