How to Make It
In a large saucepan, heat the oil over moderately low heat. Add the onion, carrot, and garlic and cook, stirring occasionally, until the onion is translucent, about 5 minutes. Add the broth and dill seeds and bring to a boil. Reduce the heat and simmer, covered, for about 20 minutes.
Meanwhile, put the potatoes in a medium saucepan of salted water. Bring to a boil, reduce the heat, and simmer until tender, about 15 minutes. Drain the potatoes and put them back into the saucepan along with 3/4 teaspoon of the salt and a pinch of pepper. Mash the potatoes over very low heat, gradually incorporating the butter and 3/4 cup of the cream. Keep warm.
Add the corn and 1/2 teaspoon of the salt to the broth and simmer, covered, until the corn is just tender, about 15 minutes. In a food processor or blender, puree the chowder and then pour it back into the saucepan. Add the shrimp and the remaining 3/4 teaspoon salt. Bring to a simmer and cook until the shrimp are almost done, about 1 minute. Stir in the remaining 1/4 cup cream, the parsley, and 1/8 teaspoon pepper and bring just back to a simmer. Reheat the potatoes, if necessary. Spoon them into the center of four bowls and pour the chowder around them.