Fill a large pot with water, adding a generous amount of salt, and bring it to a rolling boil. Add 1 lb of bucatini and cook until just shy of al dente, about 8-10 minutes. Reserve 2 cups of pasta water before draining.

In a large skillet, melt 4 tablespoons of unsalted butter over medium heat. Swirl the pan gently while the butter melts, observing for a nutty aroma and deep golden brown color, about 3-5 minutes.

Add 1 cup of reserved pasta water to the browned butter. It will bubble; stir continuously and bring to a gentle simmer. Gradually add the remaining 2 tablespoons of butter, stirring until melted.

Add the cooked bucatini to the skillet with 1/4 cup of Parmesan cheese, lemon juice, and zest. Toss and cook for an additional 3-5 minutes over medium heat, adjusting consistency with reserved pasta water if needed.

Remove from heat and stir in 3 tablespoons of minced dill. Season with kosher salt and black pepper to taste. Serve warm, garnished with additional Parmesan cheese.