Bring a large pot of salted water to a boil. Cook linguine according to package directions until al dente. Reserve 1 cup pasta water, then drain and set aside.

While pasta cooks, pat shrimp dry with paper towels. Toss with olive oil, salt, pepper, and red pepper flakes. Heat a large skillet over medium-high heat. Cook shrimp in a single layer for 1-2 minutes per side until pink and opaque and internal temperature reaches 145°F (63°C). Transfer to a plate.

Reduce heat to medium. In the same skillet, melt butter. Add garlic and cook for 30 seconds until fragrant, stirring constantly. Pour in heavy cream and bring to a gentle simmer, scraping up any browned bits from the pan.

Reduce heat to low. Whisk in Parmesan, lemon zest, and lemon juice. Stir until cheese has melted and sauce is smooth. Season with a pinch of salt and pepper. Add the sliced basil and stir to combine.

Add the drained pasta and cooked shrimp to the skillet. Gently toss with tongs until everything is coated in the sauce, adding more pasta water if needed to loosen. Taste and adjust seasoning. Serve immediately in bowls, garnished with extra basil, lemon slices, and a sprinkle of Parmesan.