Combine 1 egg and water in a small mixing bowl; beat with a wire whisk. Add flour and 1/4 teaspoon salt, stirring well.
Turn dough out onto a lightly floured surface, and knead 2 minutes. Cover and let rest 20 minutes.
Combine reserved chicken, spinach, lightly beaten egg, breadcrumbs, onion, salt, thyme, and nutmeg in a small mixing bowl; mix well.
Roll dough to 1/16-inch thickness on a lightly floured surface; cut with a 2-inch biscuit cutter. Place 1/8 teaspoon chicken mixture in center of half of the dumplings. Moisten edges, and cover with remaining dumplings; seal edges of each dumpling with tines of a fork.