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 sturdy sharp paring knife, cutting through the shell, and scrape out the vein. Rinse the shrimp and pat dry.
Pour ¼ cup of the olive oil into 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 the 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 olive oil into 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 the remaining 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.