In the bowl of a stand mixer fitted with the paddle attachment, mix together the flour and salt. Add the beaten egg, milk, and butter. Remove the paddle attachment and replace with the dough hook. Knead dough until smooth, about 5 minutes. Turn out onto a lightly floured surface and cover with a clean kitchen towel. Let rest 10 minutes.
Divide dough into 4 equal pieces and roll each piece out to 1/8 or 1/4 inch thickness. Cut into desired lengths and shapes. (a pizza cutter works really well to cut them into strips)
Place on a wire rack and allow to air dry, at least 2 hours. When the noodle are dry you can break the dry noodle into smaller pieces if desired.
To cook fresh pasta, in a large pot with boiling salted water cook until al dente.