Melt the butter in heavy saucepan. Add the shallot and sprinkle with the ground coriander. Sauté for 2 minutes, stirring frequently.
Add stock, carrots and parsnip. Bring to a boil, reduce heat, and simmer, covered until vegetables are tender, 35 minutes.
Process the mixture in 2 cup batches in food processor until smooth.
Return mixture to the saucepan, add the cream, and heat through. Season to taste, then serve hot or cold, garnished with fresh coriander and fresh chives.