Bring chicken stock to a boil. Cook chicken breasts until no longer pink in the center (15-20 minutes). Remove chicken, cool, and cut meat from bone. Keep chicken stock at a low simmer.

Using a stand mixer with a dough hook, mix flour and salt together on low. Gradually add eggs and water until the dough holds together.

Split dough in half. Roll one half to 1/8-inch thickness on a floured surface. Cut into noodles (2-3 inches long, 1/4-inch wide) using a sharp knife or a fettuccine cutter. Repeat with the other half.