Cook carrots in a 6-quart pot of boiling salted water , uncovered, until very tender, 20 to 25 minutes.
While carrots are boiling, peel potatoes and cut into 1/2-inch pieces.
Transfer cooked carrots with a slotted spoon to a food processor. Add potatoes to boiling water and cook, uncovered, until tender, about 10 minutes, then drain in a colander.
While potatoes are cooking, purée carrots in food processor with 1/4 cup cream until smooth, about 2 minutes.
Heat butter and remaining 1/4 cup cream in pot over moderate heat, stirring, until butter is melted, then force potatoes through ricer into pot. Add carrot purée, sea salt, and pepper to taste and stir until combined well.
Cooks' note: Carrot and potato purée can be made 1 day ahead and chilled, covered. Reheat in a microwave or double boiler.