In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour and salt.
Mix in the eggs and knead to bring the dough together. Slowly add water if needed to make a smooth and stiff dough.
Once smooth, wrap the dough in plastic or place in a covered bowl and allow to rest at room temperature for at least 30 minutes and up to an hour.
Divide the dough in half. Keep one wrapped and place the other on a lightly floured surface.
Roll the dough by hand with a rolling pin or use a pasta machine, flouring the dough as needed to prevent sticking. Roll until about 1/16 inch (1.5 millimeters) thick or to the thinnest setting on the pasta machine.
Dust the sheet of dough lightly with flour and loosely fold it up to make the length shorter than your knife.
Use a sharp knife to cut the noodles into 1/4 inch (6 millimeters) wide ribbons.
Unroll the noodles and separate to prevent sticking. Arrange in small nests in a single layer on a parchment-lined baking sheet. Repeat with remaining half of dough.
In a small bowl, combine the ground poppy seeds and powdered sugar.
Bring a large pot of salted water to a boil. Add the noodles, in batches if needed to avoid overcrowding, and cook until they rise to the surface and are just tender, 1-2 minutes (longer for dried). Drain well and divide between two bowls.
Top each bed of noodles with the poppy seed powdered sugar mixture.
Drizzle with the melted butter.
Serve immediately.