Place carrot and potato in a large saucepan; add water to cover. Bring to a boil; cover, reduce heat, and simmer 25 minutes or until very tender. Drain well. Process half of potato and carrot in a food processor until smooth.
Place butter in a small skillet. Cook over medium heat 3 minutes or until butter solids turn light brown, stirring often. Add brown butter and half-and-half to carrot puree. Add remaining half of carrot and potato, salt, and remaining ingredients; process until smooth.
Note: Beurre noisette is French meaning " browned butter." Don't be tempted to substitute margarine; it won't have the same flavor or consistency. Cook carefully to develop the light hazelnut ("noisette") color.