Bring a large pot of salted water to a rolling boil. Add the linguine and cook according to package directions until al dente. Reserve 1 cup of pasta water before draining. Drain the pasta and set aside.

While the pasta cooks, pat the shrimp dry with paper towels. Season with 1/2 tsp salt and 1/4 tsp black pepper. Mince the garlic and chop the fresh basil.

Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the seasoned shrimp in a single layer (cook in batches if necessary to avoid overcrowding) and cook for 1-2 minutes per side, until pink and opaque. Remove the shrimp from the skillet and set aside.

In the same skillet (no need to clean), add 3 tablespoons of olive oil and reduce heat to medium. Add the minced garlic and red pepper flakes (if using) and cook for about 30 seconds until fragrant, being careful not to burn the garlic.

If using, pour in the white wine and deglaze the pan, scraping up any browned bits from the bottom. Let it simmer for 1-2 minutes until slightly reduced.

Stir in the diced tomatoes (undrained), vegetable broth, and sugar (if using). Bring the sauce to a gentle simmer and cook for 8-10 minutes, stirring occasionally, until it thickens slightly. Season with salt and black pepper to taste.

Add the cooked pasta and the cooked shrimp to the skillet with the sauce. Toss to combine.

Add the reserved 1 cup of pasta water, 1/4 cup at a time, until the sauce reaches your desired consistency, allowing it to coat the pasta beautifully. Stir in the fresh chopped basil, cold butter pieces, and 1/4 cup grated Parmesan cheese. Toss until the butter has melted and the cheese is incorporated, creating a creamy finish.

Divide the pasta among serving bowls. Garnish with additional fresh basil and grated Parmesan cheese, if desired. Serve immediately.