Toast sesame, mustard, and cumin seeds together in a dry 2- to 3-quart heavy saucepan over moderate heat, stirring, until fragrant and a shade or two darker, 2 to 3 minutes.
Stir in water, carrots, salt, cayenne, and 2 tablespoons oil and cook, covered, over low heat, stirring occasionally, until carrots are very tender, 20 to 30 minutes.
Puree mixture in a food processor with remaining 2 tablespoons oil until carrots are smooth (spices will still be a little coarse).