Preheat the oven to 400 degrees F.
Using the extra butter, grease a 3-quart baking dish. Set it aside.
In a Dutch oven over medium-high heat, melt 3 tablespoons of the remaining room temperature butter.
Add the carrots and the onions to the butter and cook, while stirring, until softened, about 5 minutes.
Add the mushrooms to the vegetable mixture and cook, while stirring, until tender, about 5 minutes.
Add the garlic to the vegetable mixture and cook, while stirring, until fragrant, about 2 minutes.
Add the wine and cook until slightly reduced, about 2 minutes.
Add the all-purpose flour to the vegetable mixture and cook, while stirring constantly, until golden-brown and incorporated, about 3 minutes.
Slowly add the broth to the vegetable mixture, while stirring constantly, until fully combined.
Bring the vegetable mixture to a boil and cook, while stirring constantly, until it thickens, about 2 minutes.
Add the whipping cream, the white wine vinegar, 3 tablespoons of the chives, 3 tablespoons of the parsley, the rosemary, and the thyme leaves to the vegetable mixture and stir to combine.
Add the chicken to the vegetable mixture and stir to combine.
Season the chicken mixture with the salt and the black pepper, as needed.
Cover the chicken mixture and transfer it from the heat.
In a medium bowl, add the self-rising flour and the sugar and whisk to combine.
In a small bowl, add the buttermilk and 1/2 cup of the remaining melted butter and whisk to combine.
Add the buttermilk mixture and the bacon to the flour mixture and stir until just combined into a dough. Do not overmix. The dough should pull away from the sides of the bowl.
Uncover the chicken mixture and place it over medium-high heat.
Cook the chicken mixture, while stirring constantly, until bubbly and hot, about 2 minutes.
Spoon the chicken mixture into the prepared baking dish.
Drop the biscuit dough by the level 1/4-cupful over the chicken mixture, keeping the dollops about 1/2-inch apart.
Bake until the top is browned and the filling is bubbly, about 30-35 minutes.
Serve garnished with the extra chives and the extra parsley.