Peel the heads and shells off the shrimp, reserving both for the shrimp broth. (If the shrimp are in the middle of their spawn, says Hayward, clusters of gray eggs may be present that will not adversely affect the broth.) Transfer the shrimp to a bowl, cover, and refrigerate them until the chowder base is completed. Place the shrimp shells and heads in a large pot and add 10 cups cold water. Bring to a simmer over high heat, then reduce to low and gently simmer for 5 minutes, skimming off any foam that rises to the surface. Strain the broth through a fine sieve and set aside.
Now make the chowder base. Cook the bacon in a small pot of simmering water for 1 minute. Drain. Heat a medium pot over medium heat, add the bacon, and cook, stirring occasionally, until it releases some of its fat. Add potatoes and leeks, stir well, then reduce heat to medium-low and cook, covered, stirring occasionally, for 5 minutes. Add 3 cups of the reserved shrimp broth (freeze remainder for another use) and simmer, covered, until potatoes are tender, 8-10 minutes. Remove the chowder base from the heat and cover to keep warm.
Melt the butter in a large skillet over medium-high heat. Raise the heat to high, add the chilled shrimp and cream, stir well, and bring to a boil. Let boil for 30 seconds. Add the shrimp mixture to the chowder base and stir gently to combine. Cover and let rest for 10 minutes. Season with salt, a generous amount of black pepper, and the cayenne. Ladle into warm soup bowls and sprinkle the chives on top of each.