Pare the mirlitons and peel the shrimp. Put the trimmings, shrimp shells and heads, and the bay leaf into a small saucepan with two cups of water. Bring up to a light boil, then reduce to a simmer. Keep the simmer going for 20-30 minutes, during which you can do the next step.
Dice the mirlitons. In a large saucepan, melt the butter and whisk in the flour. Cook and stir into a blond roux for two minutes. Add all the vegetables except the mirlitons and cook over low heat for five minutes, until all vegetables are soft.
Stir the shrimp and mirlitons into the vegetables. Add the wine and bring to a boil for two minutes. Strain the stock from the shrimp shells into the saucepan along with the crab boil, and stir.
Warm the cream and stir into the soup. Bring to a simmer and cook about 30 minutes, stirring occasionally. Add salt and pepper to taste.