Preheat the oven to 400 degrees F.
Butter a 3-quart ceramic or glass baking dish.
In a Dutch oven over medium-high heat, melt 3 tablespoons of the butter.
Add the carrots and the onion to the melted butter and cook, for about 5 minutes.
Add the mushrooms to the veggie mixture and sauté until tender, about 5 minutes.
Stir the garlic into the veggie mixture and sauté until fragrant, about 2 minutes.
Add the wine to the veggie mixture and cook for about 2 minutes.
Sprinkle the veggie mixture with the all-purpose flour and cook, stirring constantly, for about 3 minutes.
Slowly add the broth to the veggie mixture, stirring constantly.
Bring the mixture to a boil and continue to stir constantly until thickened, about 3 minutes.
Stir the whipping cream, the white wine vinegar, the chives, the parsley, the rosemary, and the thyme into the thickened veggie mixture.
Stir the chicken into the seasoned veggie mixture and season with the salt and the pepper.
Cover the Dutch oven and carefully transfer it away from the heat.
In a medium bowl, whisk together the self-rising flour and the sugar.
In a small bowl, stir together the buttermilk and 1/2 cup of the melted butter.
Stir the buttermilk mixture and the bacon into the flour mixture until the dough pulls away from the side of the bowl.
Return the chicken mixture to medium-high heat, cooking while stirring constantly, until bubbly and hot, about 2 minutes.
Spoon the chicken mixture into the prepared baking dish.
Drop the dough by 1/4 cupful's, 1/2-inch apart, onto the chicken mixture.
Bake, uncovered, until browned and bubbly, about 30-35 minutes.
Serve with the extra chives and the extra parsley.