Bring a large pot of salted water to a boil and cook the linguine 1 minute less than the package directs, until just al dente, reserving 1 cup of pasta water before draining.
Pat the shrimp dry and season with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Heat 2 tablespoons butter and 2 tablespoons olive oil in a large skillet over medium-high heat.
Add the shrimp in a single layer and cook 1 to 2 minutes per side until pink and curled into a C shape, then transfer to a plate.
Lower the heat to medium, add the remaining olive oil, garlic and red pepper flakes, and cook 30 seconds until fragrant but not browned.
Pour in the wine, scraping up the browned bits, and simmer 2 to 3 minutes until reduced by half.
Stir in the lemon juice and remaining 4 tablespoons butter, whisking until the sauce turns glossy.
Add the drained linguine to the skillet, tossing with the sauce and 1/4 cup reserved pasta water, adding more a splash at a time until the noodles are silky and coated.
Return the shrimp to the pan, toss, sprinkle with parsley, and serve immediately with lemon wedges.
Good to Know
Devein and peel the shrimp the night before and keep them in the fridge; the dish itself does not hold well once sauced, so cook it to order.