Recommended equipment: A heavy-bottomed sauté pan, 10- to 12-inches diameter, for the sauce; a heavy-bottomed 13- to 14-inch skillet for searing the shrimp

Without removing any of the shell, remove the vein (digestive tract) that runs inside the curving back of each shrimp: Slice open the back with a sharp, sturdy paring knife, cutting through the shell, and scrape out the vein. Rinse the shrimp and pat dry.

Pour ¼ cup of the olive oil in the sauté pan and set over medium-high heat. Scatter in the garlic, cook until sizzling, then stir in the shallots. When they’re sizzling, stir in ¼ teaspoon of the salt and ¼ cup of the wine. Cook, stirring frequently, until the wine is nearly completely evaporated and the shallots have softened. Drop in the tomato paste and stir it around the pan for a minute, coating the shallots and caramelizing.

Pour in the rest of the wine, bring to a boil quickly, then add the water and ¼ teaspoon salt, stirring. Bring to a boil, then reduce the heat and let the sauce bubble gently and reduce for about 5 minutes while you sear the shrimp.

Pour 2 tablespoons of olive oil in the wide skillet and set over high heat until very hot. Scatter the shrimp in the pan, toss them in the oil and season with ½ teaspoon salt. Cook for just a minute or slightly longer, until the shells are lightly colored and the flesh underneath is opaque, then turn off the heat.

With the sauce still bubbling, slide in the seared shrimp and tumble to coat them all with sauce. Stir in the coarsely ground pepper, then the tablespoon of bread crumbs — use more crumbs if the sauce is thin. Cook for another 2 minutes, then turn off the heat.           

Drizzle over the remaining 2 tablespoons olive oil — or more to taste — and incorporate it well, tumbling the shrimp in the pan. Sprinkle the parsley on top and serve immediately.

Rinse the cherry tomatoes and pat them dry. Rinse the basil leaves and pat dry.

Drop the tomatoes into the blender jar or food processor bowl followed by the garlic clove, the almonds, basil leaves, peperoncino and ½ tsp salt. Blend for a minute or more to a fine purée; scrape down the bowl and blend again if any large bits or pieces have survived.

With the machine still running, pour in the olive oil in a steady stream, emulsifying the purée into a thick pesto. Taste and adjust seasoning. (If you’re going dress the pasta within a couple of hours, leave the pesto at room temperature. Refrigerate if for longer storage, up to 2 days, but let it return to room temperature before cooking the pasta.)

To cook the spaghetti, heat 6 quarts of water, with 1 tablespoon salt, to the boil in the large pot. Scrape all the pesto into a big warm bowl.

Cook the spaghetti al dente, lift it from the cooking pot, drain briefly, and drop onto the pesto. Toss quickly to coat the spaghetti, sprinkle the cheese all over, and toss again. Serve immediately in warm bowls.