In a bowl, combine the shrimp with 2 tbsp olive oil, 4 cloves minced garlic, and 1 tsp salt. Toss well and let the shrimp sit in the fridge while preparing the rest of the dish.
Heat 2 tbsp oil and 2 tbsp butter in a large deep pot or Dutch oven over medium heat. Add the shallots and season with a generous pinch of salt. Cook for 10–15 minutes, stirring occasionally and deglazing with splashes of water when needed, until caramelized. Deglaze the pan with a small splash of chicken stock, scraping up any browned bits. Remove the shallots from the pan and set aside.
Increase the heat to medium-high. Add a little more oil to the pan. Add the marinated shrimp to the pan and sear for 1–2 minutes per side until pink and opaque. Remove from the pan and set aside.
Reduce the heat to medium and add the tomato paste to the pan. Cook for 2–3 minutes, stirring, until darkened and caramelized. Deglaze with ½ cup of chicken stock, stirring to combine. Add the garlic and cook for 1 minute until fragrant. Stir in the crushed tomatoes and let simmer for 5 minutes. Add the caramelized shallots back in. Season with a generous pinch of salt.
Pour in the remaining chicken stock and 1 cup of heavy cream, then bring to a gentle simmer. Add the penne and parmesan rind, sttirring to ensure it's submerged in the liquid. Cover and cook for 15-20 minutes, stirring occasionally, until the pasta is tender. This can take up to 25 minutes, it all depends on the pasta you use, but definitely check on it at 15 minutes to avoid overcooking!
Once the pasta is nearly done, return the shrimp to the pan. Stir in the remaining 1/3 cup of cream, Parmesan cheese (I put a measurement in the recipe but I just grate to taste,) and fresh chopped basil. Taste and adjust seasoning if needed.
Serve hot, garnished with additional basil. ENJOY!
