Melt the butter in a 4-quart heavy saucepan over medium heat and cook the shallot, stirring, until translucent, about 4 minutes. Add the squash, coriander, cumin, 1/2 teaspoon each salt and pepper. Stir until coated. Pour in the broth and bring to a simmer and cook, uncovered, until the squash is very tender, 25 to 30 minutes.
Carefully puree the soup with an immersion blender or in a stand blender, in batches, until very smooth. Return the soup to the saucepan and stir in the cream. Season salt and pepper. Reheat the soup before serving if necessary.
Bring a small saucepan of water to a boil. Add the parsley and cook, uncovered, until bright green, 30 to 45 seconds. Transfer with a slotted spoon to a bowl of ice water and then drain and pat dry. Puree in a blender with the grapeseed oil until the oil is bright green, about 1 minute. Strain the parsley oil through a fine-mesh sieve. Do not press on the solids. Whisk the harissa and 1 tablespoon water together in a small bowl until smooth.
Whisk the oil, lemon juice, ginger, 1 teaspoon salt and 1/2 teaspoon pepper together in a medium bowl. Add the crab, cilantro and mint and gently toss to combine.
Divide the hot soup evenly among 4 serving bowls and mound some crab salad in the middle of each bowl. Drizzle each bowl with parsley oil and harissa.
Harissa is a North African condiment made from spices and chilies. It can be found in specialty food markets.