In a saucepan over medium heat, melt the butter. Add the shallot and cook, stirring occasionally, until the shallot is translucent and tender, about 3 to 5 minutes.
Add the flour, parsley, salt, and pepper, stirring constantly for 2 minutes. This will prevent the flour from tasting raw later.
Stir in the shellfish stock, milk, and cream. Stirring constantly, bring the mixture to a boil. Boil for 1 or 2 minutes until the mixture starts to thicken.
Add the raw shrimp and bring back to a boil. Reduce the heat and simmer, stirring frequently, until the shrimp is cooked through and pink, about 3 minutes.
Serve with the chopped chives.