1. Heat oven to 400 degrees. Prick sweet potatoes. Place on a baking sheet and cook until soft, about 40 minutes. Let cool.

2. Peel sweet potatoes, cut into chunks, and set aside. Melt 2 tablespoons butter in an 8-inch skillet over medium heat. Reduce heat to medium low, and add shallots; cook, stirring occasionally, until caramelized, 6 to 8 minutes. Add vinegar; cook 2 minutes. Stir in ginger, mustard, cayenne, salt, and pepper. Cook over low heat 2 to 3 minutes.

3. Place sweet potatoes in a food processor; add shallot mixture; process until smooth. Transfer mixture to a heavy saucepan. Over low heat, cook 1 hour, stirring often, until mixture takes on a deep, rich color. Cool completely.

4. Transfer mixture to an electric mixer. Add remaining 4 tablespoons butter in small pieces; whip until fluffy. Serve.