Boil pasta in salted water until nearly al dente (pasta will finish cooking in the sauce) and reserve 2 cups pasta cooking water. Drain pasta and set aside for a moment.

In a large skillet over medium heat, melt 4 tablespoons butter, swirling pan occasionally until butter is a deep golden brown, about 3-5 minutes of cooking.

Add 1 cup pasta cooking water to butter mixture and bring to a simmer over medium heat. Add remaining butter, 1 tablespoon at a time stirring constantly until sauce is creamy.

Add cooked pasta, Parmesan, lemon juice, and zest to sauce and continue to cook over medium heat, stirring occasionally until sauce is thickened and creamy, about 3-5 minutes. Add a few splashes of remaining pasta water as needed to thin sauce.

Remove pasta from heat, stir in dill, and season with salt and freshly ground black pepper as needed. Serve pasta warm with additional Parmesan on top and enjoy!