Bring a large pot of salted water to a boil. Add linguine and cook according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain.

While the pasta cooks, pat the shrimp dry with paper towels and season with salt and pepper.

Heat olive oil and butter in a large skillet over medium-high heat. Add shrimp in a single layer and cook for about 2 minutes per side until pink and opaque. Transfer the shrimp to a plate.

In the same skillet, add garlic and cook for 30 seconds until fragrant. Add cherry tomatoes and a pinch of salt; sauté for 3–4 minutes until tomatoes begin to break down.

Lower the heat to medium. Stir in heavy cream and reserved pasta water. Simmer for 2 minutes until the sauce slightly thickens.

Add the cooked pasta, shrimp, lemon zest, and cheese to the skillet. Toss to combine, adjusting seasoning with salt, pepper, and red pepper flakes, if using. Add lemon juice to taste.

Remove from heat, stir in fresh parsley, and serve immediately, garnished with extra Parmesan if desired.