Toss shrimp with 1/4 teaspoon salt and set aside. Pour tomatoes in colander set over large bowl. Pierce tomatoes with edge of rubber spatula and stir briefly to release juice. Transfer drained tomatoes to small bowl and reserve juice. Do not wash out colander.
Heat 1 1/2 teaspoons vegetable oil in 10-inch skillet over high heat until shimmering. Add shrimp shells and cook, stirring frequently, until they begin to turn spotty brown and skillet starts to brown, 1 to 2 minutes. Remove skillet from heat and carefully add wine. When bubbling subsides, return pan to heat and simmer until wine is reduced to about 2 tablespoons, 1 to 2 minutes. Add reserved tomato juice and simmer to meld flavors, 2 1/2 minutes. Pour contents of skillet into colander set over bowl. Discard shells and reserve liquid. Wipe out skillet with paper towels.
Heat remaining 1 tablespoon vegetable oil, garlic, pepper flakes, and oregano in now-empty skillet over medium heat, stirring occasionally, until garlic is straw-colored and fragrant, 30 to 60 seconds. Add anchovy and stir until fragrant, about 15 seconds. Remove from heat. Add drained tomatoes and mash with potato masher until coarsely pureed. Return to heat and stir in reserved tomato juice mixture. Increase heat to medium-high and simmer until mixture has thickened, about 2 1/2 minutes.
Add shrimp to skillet and simmer gently, stirring and turning shrimp frequently until they are just cooked through, 2 to 2 1/2 minutes. Remove pan from heat. Stir in basil, parsley, and pepperoncini and brine and season with salt to taste. Drizzle with olive oil and serve.