Combine the flour and salt in a large bowl, then make a well in the center and add in the eggs.
Using a fork combine the eggs into the flour mixture until slightly sticky.
Roll out the dough on a floured surface, adding in more flour if necessary and knead for about 5 minutes, forming into a ball.
Cover the dough ball with plastic wrap and place this in the fridge for at least 15 minutes, but up to 24 hours.
Remove the dough from the fridge and roll out until about 1/4" thick, then cut them to the width you prefer.
Continue to add more flour if needed to avoid sticking and cut them. Place each noodle on a plate or in a pan.
Let them sit uncovered for 1 hour until they have dried out.
Once the noodles are done, add the noodles, chicken, cream of mushroom soup, and butter to a large stockpot or French oven.
Cover and let them warm up to a low boil.
At this point, if the soup you used is more of a runny consistency, carefully whisk in the flour to thicken it, and then let this boil for 20-25 minutes.
Serve as is, or over mashed potatoes.