In a large soup pot or Dutch oven, heat the olive oil over medium-high heat. Add the carrots and onion and cook until softened, about 5 minutes. Add the garlic and cook for another 30 seconds. Add the chicken broth, chicken, and bay leaves and bring to a gentle boil. Reduce the heat and let simmer for 15 minutes.

While the soup is simmering, chop the bacon into pieces about ½ inch. Place in a large skillet and cook over medium heat until it has rendered its fat and the bacon is crispy. Remove the bacon pieces with a slotted spoon, and add the mushrooms. Raise the heat to medium-high and cook the mushrooms, stirring occasionally, until they are browned, about 8 minutes. Take off the heat, add the bacon back to the pan and add the green onions. Season to taste with salt and pepper and reserve until you serve the chicken and dumplings.

In a mixing bowl, whisk together the flour, baking powder, baking soda, ¾ teaspoon salt, and the sugar. Add the melted butter and stir with a fork. Starting with about ¾ cup, stir in the buttermilk. Keep adding buttermilk, a little at a time, until the mixture forms into a soft dough.

Drop tablespoons of the batter onto the top of the simmering soup, cover the pan and let simmer for 15 minutes.

Serve in bowls topped with the bacon mixture.