Bring a large pot of water to a rolling boil. Add 1 tablespoon salt. Add 12 oz linguini and cook according to package instructions until just shy of al dente (about 9–10 minutes). Reserve 1 cup of the pasta cooking water, then drain the pasta and set aside.

Shrimp

Season shrimp

Pat the shrimp dry with paper towels. In a bowl, toss shrimp with 1 tsp kosher salt, 1 tsp black pepper, 1 tsp paprika, and 1 tbsp olive oil until evenly coated.

Sear shrimp

Heat a large saute pan over medium-high heat until hot. Add the seasoned shrimp in a single layer and cook 1.5–2 minutes per side until just opaque and lightly golden. Remove shrimp to a plate and set aside (they will finish cooking in the sauce).

Pomodoro Sauce

Sweat aromatics

In the same large saute pan, reduce heat to medium and add 2 tbsp extra-virgin olive oil. Add the thinly sliced garlic and 1 finely chopped shallot. Cook, stirring frequently, until fragrant and the shallot is translucent, about 2–3 minutes. Do not let the garlic brown. Add 1 tsp crushed red pepper flakes and cook 30 seconds.

Add tomatoes

Stir in the 28 oz crushed tomatoes and 1 tbsp tomato paste. Bring the sauce to a gentle simmer, scraping any browned bits from the pan. Reduce heat to low and simmer, uncovered, for 10–12 minutes to thicken slightly.

Season sauce

Stir in 8 torn basil leaves, 1 tsp sugar (if using), 1 tsp kosher salt, and 1 tsp freshly ground black pepper. Taste and adjust seasoning. If sauce is too acidic, add a pinch more sugar. Keep sauce at a gentle simmer.

Combine & Finish

Finish sauce with shrimp and pasta

Return the pre-seared shrimp to the pan with the simmering pomodoro. Add the drained linguini and 1/2 cup of the reserved pasta water. Toss to combine over medium heat, adding more reserved water a few tablespoons at a time if the sauce seems dry, until the pasta is coated and perfectly al dente, about 1–2 minutes. Stir in 1 tbsp unsalted butter to enrich the sauce.

Add cheese and herbs

Remove the pan from heat. Stir in 1 cup grated Parmesan, the zest and juice of 1 small lemon (about 1 tbsp juice), 2 tbsp chopped parsley, and 1 tsp finishing olive oil. Toss to emulsify the sauce and create a glossy coating on the pasta. Adjust seasoning with salt and pepper to taste.

Serve

Divide pasta among 4 plates or bowls. Spoon any remaining sauce and shrimp over the top. Garnish with additional basil leaves and extra Parmesan if desired. Serve immediately.