In a small saucepan, combine the rice with 1 1/2 cups water. Bring to a boil, cover, lower the heat and simmer until tender, about 20 minutes; fluff with a fork. Cover to keep warm.
Meanwhile, in a large saucepan, melt 2 teaspoons 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 teaspoons 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 the chives. Serve over the rice.