To poach the chicken, in a large saucepan, add the breasts and the chicken stock to cover. Add the bouquet garni. Bring to a boil over high heat, then decrease the heat to low. Simmer, skimming off the foam occasionally, until the chicken is tender, 10 to 15 minutes. (If the stock is cloudy, don't worry; it's simply protein clarified from the stock. Just ignore it or strain it out.) Transfer the poached chicken to a warm plate; reserve the stock. Cover with a lid and set aside.

To prepare the dumplings, in a bowl, combine the flour, cheese, baking powder, parsley, and ¾ teaspoon of the salt. In a small saucepan, bring the milk and butter to a simmer over low heat; season with black pepper. Add the milk mixture to the dry ingredients and stir to combine.

In a second large saucepan, heat the oil over medium heat. Add the onion, carrots, and sweet potato. Cook until the onions are translucent, 3 to 5 minutes. Add the garlic and cook until fragrant, 45 to 60 seconds. Add the reserved stock and bring to a boil over high heat. Decrease the heat to low. Using a small ice cream scoop or tablespoon, drop the dough, about 1 tablespoon at a time, into the simmering stock. Cover and simmer until the dumplings are cooked through and the vegetables are tender, about 20 minutes.

To assemble, add the reserved chicken and cook just until heated through, about 5 minutes. Stir in the spinach; cover and continue cooking for an additional 30 to 45 seconds. Add the red pepper flakes, taste and adjust for seasoning with salt and pepper.

To serve, ladle into shallow bowls and garnish with additional cheese; serve immediately.