Pour the raw, peeled shrimp onto a thick layer of paper towels and press another towel firmly over the top. Pro Tip: Removing all surface moisture is the most critical step. If shrimp enter a hot pan wet, they immediately bleed water and steam in their own juices, which leaves them rubbery and grey instead of developing a crisp, caramelized outer crust.
Heat the olive oil in a large skillet over medium-high heat. Toss the dried shrimp into the sizzling pan, seasoning them with a pinch of salt and pepper. Sauté for 1 to 2 minutes per side just until they curl slightly and turn opaque, then immediately transfer them to a side plate. Do not overcook them here.
Reduce the skillet heat to medium. Drop the unsalted butter and minced garlic directly into the residual pan oil. Cook for 30 to 45 seconds, stirring constantly, until the butter melts completely and the garlic is fragrant but still pale yellow.
Pour the white wine straight into the hot skillet. Use a wooden spatula to aggressively scrape up any caramelized bits stuck to the bottom of the pan. Simmer the liquid for 3 to 4 minutes until it has reduced by half. This boils off the raw alcohol bite, leaving behind a concentrated, acidic fruit baseline that cuts through the upcoming heavy fats.
Pour the heavy whipping cream into the wine reduction in a slow, steady stream, whisking constantly to emulsify the dairy and pan fats together. Lower the heat to medium-low and simmer gently for 5 minutes until the sauce naturally thickens enough to coat the back of a spoon.
Stir the freshly grated Parmesan cheese into the warm cream sauce until completely melted and smooth. Taste the sauce now and adjust with extra salt and pepper if needed.
Slide the cooked shrimp and any pooled juices from their plate back into the skillet. Toss thoroughly for 60 seconds to coat every shrimp in the velvety sauce and bring them back up to serving temperature. Serve immediately over your favorite pasta or with crusty bread.