Peel and devein the shrimp, reserving the shells and tails in a small bowl as you go. Place the cleaned shrimp in a large bowl and sprinkle with the salt; toss and set aside.

Set a colander over a large bowl. Pour the tomatoes and their juices into the colander. Use the side of a rubber spatula to pierce the tomatoes; press down and stir to release the juices inside of the tomatoes. Transfer the drained tomatoes to a small bowl, reserve the juices, and set the colander aside without washing it.

Heat 1 tablespoon of the vegetable oil in a 12-inch skillet over high heat. Once the oil starts to shimmer, add the shrimp shells and cook until they turn brown in spots, stirring often, 2-4 minutes. Carefully add the wine to the skillet and let it bubble until it is reduced by at least three-quarters, 2-4 minutes. Pour in the reserved tomato juice, then reduce heat and allow to simmer for 5 minutes.

Set the colander back over the large bowl and pour everything in the skillet into the colander. Press down gently on the shells to drain any liquid that may be hanging out inside of them. Discard the shells and save the shrimp-tomato broth.

If the skillet has any residual pieces of shell on the bottom or sides, use a paper towel to wipe it out. Set the skillet back over medium heat and add the remaining 2 tablespoons of oil. Add garlic, basil, chile flakes (use less if you’re sensitive to spicy foods), and oregano and saute, stirring occasionally, until garlic just starts to color and smells good, 1 to 2 minutes. Add anchovies and stir for another 30 seconds.

Add the reserved drained tomatoes and use a potato masher to smash them until only a few large chunks remain. Stir in the reserved shrimp-tomato broth. Increase the heat to medium-high and allow everything to simmer until mixture has thickened slightly, about 5 minutes.

Add the shrimp to the skillet and simmer gently, stirring and turning shrimp often, until they are just cooked through, 4 to 5 minutes.

Remove the pan from the heat. Stir in the parsley, pepperoncini and brine.

Serve over warm pasta or with a loaf of crusty bread for mopping up the glorious juices.