In a large saucepan, melt 2 tsps butter over medium heat. Add the shrimp shells and cook, stirring until crisp, about 5 minutes. In a small bowl, whisk the milk with the cornstarch, then whisk into the shrimp shells. Bring to a simmer, whisking, then cook for 1 minute. Strain the mixture into a bowl, pressing the shrimp shells to get all the liquid, discard the shells. Wash and dry the saucepan.
In the saucepan, melt the remaining 2 tsps butter over medium-low heat. Add the onion and cook, stirring frequently, until softened, about 5 minutes. Stir in the flour for 2 minutes. Slowly whisk in the milk mixture and bring to a boil. Lower the heat and simmer for 1 minute.
Stir in the shrimp and sherry and cook, stirring until the shrimp is firm, about 2 minutes. Season with salt and pepper, stir in chives.