12 large shrimp—shelled, deveined and halved lengthwise
1 tablespoon coarsely chopped tarragon
Lemon wedges, for serving
In a medium saucepan, cover the parsnips with the milk and water, add a pinch of salt and bring to a boil. Simmer over moderately low heat until the parsnips are tender, about 10 minutes; drain, reserving 1/4 cup of the cooking liquid. Transfer the parsnips and the reserved liquid to a food processor and puree. Return the puree to the saucepan, season with salt and pepper and keep warm.
In a large skillet, melt the butter. Add the shrimp, season with salt and pepper and cook over moderate heat, stirring, until the shrimp are pink and just white throughout, about 3 minutes. Stir in the tarragon. Spoon the parsnip puree onto plates, top with the shrimp and drizzle with the butter. Serve with lemon wedges.