1. Cook the Pasta: Bring a large pot of heavily salted water to a boil. Add the pasta and cook according to package directions until al dente. Before draining, reserve at least 1 cup of the pasta water.

2. Sauté Aromatics: While the pasta cooks, melt 1 tablespoon of butter in a large skillet over medium heat. Add the diced shallot and cook until softened, about 3 minutes. Add the minced garlic and cook for another 30-60 seconds until fragrant but not browned.

3. Build the Sauce: Pour in the heavy cream, lemon juice, and lemon zest. Bring the mixture to a very gentle simmer and let it cook for 2-3 minutes to slightly thicken.

4. Incorporate Cheese: Reduce the heat to low. Gradually whisk in the freshly grated Parmesan cheese until completely melted and smooth. Season generously with salt and pepper. If the sauce is too thick, thin it with a splash of the reserved pasta water.

5. Combine and Serve: Add the drained pasta to the skillet with the sauce. Toss vigorously to coat every strand, adding more pasta water if needed to create a silky, clinging sauce. Stir in the remaining tablespoon of cold butter. Garnish with chopped parsley and extra Parmesan before serving immediately.