1 pound medium shrimp, heads on
5 tablespoons unsalted butter, divided
2 cups diced onions
1 bay leaf
4 cups (about 1 medium) peeled, seeded and diced butternut squash
2 1/2 teaspoons salt
1/8 teaspoon ground white pepper
3/8 teaspoon ground cayenne
1/4 teaspoon dried basil
1/4 teaspoon dried thyme
1/4 teaspoon minced garlic
1 quart heavy cream
1 cup half-and-half
1/2 teaspoon fresh basil, very finely chopped
18 to 24 whole shrimp, butterflied and sauteed, for garnish
Shell the shrimp. Place the heads and shells in a medium pot and cover with cold water. Bring to a boil, reduce the heat and simmer 15 minutes. Strain the broth and reserve.
Heat a 4-quart saucepan over medium-high heat. Add 3 tablespoons butter, the onions and bay leaf. Cook, stirring constantly, until the onions start to brown, about 5 to 6 minutes.
Reduce the heat to medium and add the squash. Cook, stirring occasionally, until the squash begins to soften and turn brown, 7 to 8 minutes.
Reduce the heat to low and add 1 tablespoon butter and the peeled shrimp. Cook, stirring occasionally, until the shrimps turn pink, 3 to 4 minutes.
Add the salt, white pepper, cayenne, basil, thyme and garlic. Cook 3 to 4 minutes, stirring constantly and scraping the bottom and sides of the pan with a metal spoon. (This procedure will intensify the taste of the soup.) Add 1 1/2 cups reserved shrimp stock and simmer 2 to 3 minutes.
Remove the pot from the heat. Discard the bay leaf. Transfer the contents to a food processor and puree until smooth. Return the puree to a clean saucepan and add the cream and half-and-half. Bring to a boil, lower the heat and simmer 2 to 3 minutes. Just before serving, add the fresh basil and remaining 1 tablespoon butter. Top each serving with several sauteed shrimp.