Cook the pasta in a large pot of salted boiling water according to package directions until al dente. Just before draining, reserve 1 cup of the starchy pasta water.

While the pasta cooks, pat the shrimp completely dry with paper towels. Season them on both sides with 1/2 tsp salt and 1/4 tsp black pepper.

Heat 1 tbsp of olive oil in a large skillet or Dutch oven over medium-high heat. Add the shrimp in a single layer and cook for 1-2 minutes per side, just until they turn pink and opaque. Do not overcook. Remove the shrimp from the skillet and set aside on a plate.

In the same skillet, reduce the heat to medium. Add the 2 tbsp of butter. Once melted, add the finely chopped shallot and cook, stirring occasionally, for 2-3 minutes until softened and translucent.

Add the minced garlic, chopped sun-dried tomatoes, and 1 tbsp of reserved oil from the tomato jar. Cook for about 1 minute until the garlic is fragrant, stirring constantly to prevent burning.

Pour in the chicken broth to deglaze the pan, using a wooden spoon to scrape up any flavorful browned bits from the bottom. Let it simmer and reduce for about 2-3 minutes.

Reduce the heat to low. Stir in the heavy cream, dried oregano, and red pepper flakes. Bring to a gentle simmer, but do not boil.

Gradually whisk in the grated Parmesan cheese until the sauce is smooth and has slightly thickened. Taste and adjust seasoning with more salt and pepper if needed.

Add the drained pasta and the cooked shrimp (along with any juices from the plate) back into the skillet with the sauce. Toss well to coat everything evenly. If the sauce seems too thick, add a splash of the reserved pasta water until it reaches your desired consistency.

Remove from heat, stir in the fresh basil, and serve immediately. Garnish with additional Parmesan cheese and red pepper flakes if desired.