NOTE: To make shrimp stock, place shrimp heads and shells into a saucepan and cover with cold water. Bring to a boil. Reduce heat to low and simmer for 15 minutes. Strain.
Heat the butter in a heavy-duty saucepan over medium-high heat. Add the onions and bay leaf and cook, stirring constantly, until the onions become soft and clear, 3-4 minutes. Reduce heat to medium and add the butternut squash. Cook this mixture, stirring occasionally, until the squash begins to soften, 6-8 minutes.
Reduce heat to low and add the shrimp, salt, cayenne, and white pepper. Cook, stirring occasionally, until the shrimp turn pink, 2-3 minutes.
Add the shrimp stock and cook, stirring occasionally, for 6-8 minutes. If the mixture begins to stick to the pan, scrape it with a spoon and continue cooking. This will intensify the flavor of the bisque.
Remove bay leaf and discard. Transfer the squash/shrimp mixture to a food processor and puree. Return the puree to a saucepan and add the cream. Whisk until thoroughly blended. Bring to a boil. Reduce heat to low and simmer for 2-3 minutes.