Cook the pasta in boiling salted water until al dente, then drain and set aside.
Heat a large skillet over medium heat and add butter and olive oil, letting them melt together until shimmering and fragrant.
Add the minced garlic to the skillet and sauté for about 30 seconds until it becomes fragrant and golden, filling the kitchen with a rich aroma.
Place the shrimp in the skillet in a single layer and cook for 2-3 minutes on each side until they turn bright pink and are just cooked through. Remove them from the pan and set aside.
Pour in the heavy cream and stir, scraping up any browned bits from the bottom of the pan. Bring to a gentle simmer and cook for 2 minutes until slightly thickened.
Gradually stir in the freshly grated Parmesan cheese until melted and smooth, creating a luscious, velvety sauce. If it gets too thick, add a splash of pasta water to loosen it.
Return the cooked shrimp to the skillet, tossing gently to coat them in the sauce. Squeeze in lemon juice and season with salt and pepper to taste. Cook for another 2 minutes, allowing flavors to meld.
Add the cooked pasta to the skillet and toss everything together until evenly coated with the creamy sauce. If needed, loosen with a little more pasta water.
Garnish with chopped parsley and extra Parmesan if desired, then serve immediately while hot and saucy.