Bring a large pot of salted water to a rolling boil. Add a drizzle of vegetable oil, 1 tablespoon kosher salt, and the linguine; cook according to package directions until al dente (about 7–10 minutes).
While pasta cooks, heat the butter and 2 1/2 tablespoons olive oil in a large heavy-bottomed pan over medium-low heat.
Add the minced garlic and sauté about 1 minute until fragrant, being careful not to let it burn.
Add the shrimp to the pan with 1 teaspoon kosher salt and 1/4 teaspoon black pepper; sauté, stirring often, until shrimp are just pink and opaque, about 4–5 minutes.
Remove the pan from heat and stir in the chopped parsley, grated lemon zest, 1/4 cup lemon juice, lemon half-rounds, and red pepper flakes; toss to combine.
Drain the linguine in a colander and return it to the pot. Immediately add the shrimp and sauce to the pasta and toss thoroughly to coat.
Serve the linguine and shrimp hot.