Step 1: Cook the linguine according to package directions in a large pot of salted boiling water until al dente. Reserve 1 cup of pasta water before draining. Set aside.
Step 2: While the pasta cooks, pat the shrimp dry with paper towels. Season generously with salt and pepper.
Step 3: Heat 1 tablespoon of olive oil in a large skillet or Dutch oven over medium-high heat. Add half of the shrimp and cook for 1-2 minutes per side, until pink and opaque. Do not overcrowd the pan. Remove cooked shrimp to a plate. Repeat with the remaining 1 tablespoon of olive oil and the rest of the shrimp. Remove all shrimp from the pan.
Step 4: Reduce heat to medium. Add the minced shallot to the same skillet and cook for 2-3 minutes until softened. Add the minced garlic and cook for another minute until fragrant, being careful not to burn it.
Step 5: Pour in the dry white wine and deglaze the pan, scraping up any browned bits from the bottom. Let it simmer for 1-2 minutes until slightly reduced.
Step 6: Stir in the bloomed saffron threads (with their soaking liquid) and the heavy cream. Bring the sauce to a gentle simmer and cook for 3-5 minutes, stirring occasionally, until it slightly thickens.
Step 7: Stir in the 1/2 cup grated Parmesan cheese until melted and smooth. Season the sauce with salt and pepper to taste. If the sauce is too thick, add a splash of the reserved pasta water until desired consistency is reached.
Step 8: Add the cooked linguine and the cooked shrimp back into the skillet with the sauce. Toss gently to coat everything evenly. If needed, add more reserved pasta water to loosen the sauce.
Step 9: Garnish generously with fresh chopped parsley and serve immediately with extra Parmesan cheese and lemon wedges, if desired. Enjoy your delicious Shrimp Linguine with Creamy Saffron Sauce!