In a large stock pot, combine the carrots, celery, onion, bay leaves, wine, and turkey carcass. Add 7 quarts of cold water and bring to a boil over medium-high heat. Reduce the heat and simmer, covered, for 1 hour. Strain the broth and discard the solids. Let cool.
For the soup:
Heat oil in a large stock pot over medium-high heat. Add the onion and cook until starting to brown, about two minutes.
Add the carrots and sauté for four minutes. Season with salt and pepper.
Add the tomatoes, wine, and bay leaf and bring to a boil. Add two quarts of broth and return to a boil. Reduce the heat and simmer until the vegetables are tender, about 10 to 15 minutes. Season to taste with salt and pepper.
Add the turkey and spinach and simmer until the spinach is wilted, about 5 minutes. At this point, the soup may be cooled and refrigerated for up to 2 days. Bring to a simmer before continuing.
For the dumplings:
In a medium saucepan, bring 3/4 cup water, butter, salt to a boil over medium heat. When the butter has melted, remove the pan from the heat and whisk in the flour until thoroughly combined.
Return the pan to the burner and stir until the mixture pulls away from the sides of the pan.
Scrape the dough into a large bowl. Beat in the egg until the batter is smooth. Fold in the herbs. The dumpling batter may be covered and refrigerated for up to 1 day.
Drop ½ teaspoons of batter into the simmering soup until all of the batter is used. After the dumplings rise to the top, cover the pan and steam the dumplings until they have puffed up to double their size, about 4 minutes. Serve hot.