Melt butter in a large stockpot or Dutch oven set over medium-high heat. Add onion, carrots, and celery. Cook 4-5 minutes, stirring frequently, until vegetables just begin to soften.

Stir in garlic, Italian seasoning, 1/2 teaspoon salt, and a few turns of black pepper. Cook 1 minute more, just until fragrant, then pour in turkey stock. Bring mixture to a rapid simmer, then add shredded turkey meat.

To make the dumplings, combine flour, baking powder, salt, and cayenne in a medium bowl. Add buttermilk and 1/2 cup heavy cream, then stir with a rubber spatula until the mixture comes together into a shaggy dough.

Drop spoonfuls of dough directly into the simmering soup. Cover the pot and let cook for 5 minutes, then remove lid. Gently flip dumplings over, leave the lid off, and simmer for another 5 minutes.

Reduce heat to medium-low, then stir in cream and cook for 1-2 minutes, just until warmed through. Taste and season with more salt and pepper to taste. Serve piping hot with fresh herbs as a garnish, if desired.