Add in eggs, milk and water and mix until stretchy and smooth. Form mixture into a ball. If the dough is a bit dry, add in more milk 1 Tbsp at a time.
Cut two large pieces of parchment paper and lay dough between them. Roll into a 12 inch round and place it in the freezer while you finish the filling portion of the recipe (leave it between the parchment paper).
Preheat oven to 400F.
In a large oven-proof skillet, heat oil over medium heat. Add in onions and sauté until they start to soften, about 5 minutes. Once softened, add in garlic, sage, carrots, celery, and squash. Sauté until the celery begins to turn translucent, about 5 more minutes.
Pour in chicken broth; bring to a boil. Reduce to a simmer and stir constantly until the mixture begins to thicken, about 5 minutes.