Bring a large pot of salted water to a boil. Cook the linguine according to the package directions until just al dente. Before draining, reserve 1 cup of the cooking water. Drain the pasta.

Meanwhile, pat the shrimp dry and season lightly with salt and black pepper. Heat the olive oil in a 12-inch skillet over medium heat. Arrange the shrimp in a single layer, cooking in batches if necessary. Cook about 1–2 minutes per side, until the flesh is pearly and opaque throughout. Transfer to a clean plate; timing varies with shrimp size.

Reduce the heat to medium-low. Add the garlic and red pepper flakes to the skillet and stir for about 30 seconds, until fragrant but not browned. Add the cream and 1/4 cup of the reserved pasta water. Bring to a gentle simmer and cook for about 1 minute.

Reduce the heat to low. Add the Parmesan gradually, stirring until incorporated. Add the drained pasta and toss, adding more reserved pasta water a little at a time until the sauce coats the noodles.

Return the shrimp and any juices from the clean plate to the skillet and toss briefly until heated through. Remove from the heat, stir in the lemon juice, and taste for salt and pepper. Serve with basil.