Melt the butter in a large skillet or high-sided braiser over low heat, then stir in the flour until a smooth paste forms. The mixture should look pale, thick, and a little sandy, and after 30 seconds to 1 minute it should smell buttery with a faint sweet, nutty aroma but no browning.

Take the pan off the heat and whisk in 1/2 cup milk until the paste loosens and turns creamy. Once that first addition is smooth, pour in the remaining milk slowly while whisking constantly so no flour clumps settle on the bottom.

Return the pan to medium-low heat and cook the sauce, whisking often, until it thickens to the texture of runny sour cream, about 12 to 20 minutes or more depending on pan size. A wider pan can reduce and thicken a bit faster, while a deeper narrower pan may take longer, so watch the texture more than the clock.

Season with salt, then add the nutmeg or Parmesan if using and continue stirring until the sauce is fully smooth. It is ready when it coats the back of a wooden spoon and a finger dragged across the spoon leaves a clean line.