Make the noodles:

Cup of Yum
1. Mound the flour in a large wide bowl or on a work surface. Sprinkle over the salt and make a well in the middle.
2. Break the eggs into the well and mix the yolks and whites with your finger or a fork, then mix the flour with the eggs by drawing it into the center of the well with your hands, a fork, or a dough scraper; the mixture will be crumbly.
3. Sprinkle the water over and rub or cut it in. Continue to add water a tablespoon at a time, mixing after each addition, until the dough holds together but is not sticky; you may need to add up to an additional 1/3 cup water. Turn out onto a lightly floured work surface and knead the dough just until it is smooth, about 5 minutes.
4. Wrap in plastic wrap and refrigerate for at least 30 minutes, or overnight.
5. Divide the dough into 4 pieces.
6. On a lightly floured work surface, roll each piece as thin as possible with a floured rolling pin (or use a pasta machine).
7. Use a sharp knife to cut the dough into 1 1/2 to 2 inch squares.
8. Put the cut noodles on a baking sheet. Sprinkle about a tablespoon of flour over the noodles and toss lightly.

To assemble:

1. Bring a 5-quart pot of water to a boil. Add the noodles and boil until they rise to the surface and are al dente, about 5 minutes.
2. While the noodles are cooking, melt the butter in a small saucepan over medium-low heat and heat until it sizzles. Remove from the heat and cover to keep warm.
3. Drain the noodles and transfer to individual serving bowls. Top with the cheese and pour the hot butter over. Garnish with the parsley, if using, and serve immediately, passing red pepper flakes at the table.