Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the shrimp and cook, turning once, until almost cooked through, about 1 minute per side. Transfer to a plate.
Add the remaining 3 tablespoons olive oil to the skillet, then add the garlic, anchovies and red pepper flakes; cook, stirring, until the garlic is soft, about 1 minute. Add the tomatoes with their juices, the wine, oregano and 1 teaspoon salt. Bring to a simmer and cook, stirring occasionally, until thickened, about 15 minutes.
Meanwhile, bring a pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1/2 cup cooking water, then drain the pasta.
Add the parsley, pasta and shrimp to the sauce along with any collected juices from the plate and toss to combine. Stir in some of the reserved cooking water to loosen the sauce. Season with salt. Divide among shallow bowls and drizzle with olive oil; top with red pepper flakes, if desired.