Cut off the shrimp heads; peel and separate the shrimp from the heads and shells, which should be reserved. If the shrimp are large, cut them into pieces; leave small or medium shrimp whole. Chop the parsley stems; tear the leaves or leave them whole if small.

In a small skillet, sauté the garlic in 1 tablespoon olive oil until quite soft and golden, but not browned; you may have to adjust the heat or lift the skillet off the burner at intervals, shaking it until the garlic cools a bit and then returning it to the burner.

Combine the shrimp shells and heads, parsley stems, and sautéed garlic in a large skillet with 3 tablespoons olive oil. Sauté over medium heat until the mixture takes on a red-orange hue. Add the white wine and 3/4 cup water, and bring to a simmer; cover and simmer for about 10 minutes.

Place a large pot of cold water over high heat and bring to a boil for the pasta.

Meanwhile, working in batches as necessary, press the contents of the skillet through a food mill fitted with the fine cutting plate, set over a bowl. Return the red­-orange puree to the skillet, discarding the solids left behind in the food mill. Bring the puree to a simmer, adding water to dilute it if it seems too thick, and season to taste with salt and red pepper flakes. Stir in the shrimp, cooking just until they lose their raw look; keep the sauce warm.

Add salt to the boiling water and cook the linguine until al dente. Drain the linguine, reserving some of the cooking water, and transfer to the skillet. Cook for a minute or two, stirring to coat the strands with the shrimp sauce and adding cooking water as necessary for a saucy consistency. Stir in the parsley leaves.