For the broth: Place the chicken, vegetables, herbs, salt and pepper in a large dutch oven or pot and add 8 cups water. Cover and bring to a boil over medium high heat. Skim off any foam that rises to the surface. Reduce heat to a slow simmer with lid partially on and simmer for 20 minutes or so. Remove the chicken pieces to a bowl and let cool then pick the meat off the bones. Place bones back in broth and cook for another 30 minutes or so on low. Strain the broth and skim off fat if desired. Set aside.
For the stew veggies: In the dutch oven or stock pot, melt 2 tablespoons butter over medium heat and add the mushrooms, garlic and thyme, cook for 5 minutes or so until browned, add a pinch of salt and pepper. Place in a bowl and set aside. Add 1-2 more tablespoons of butter and then add the fennel, carrots and leeks and cook for about 5 minutes. Add 1/2 marsala and deglaze pan. Add 6 cups of warm stock, the chicken meat and the mushrooms to the pot, increase heat to medium then to a slow simmer. Taste and adjust seasoning if needed. If you prefer a thicker consistency, add the roux paste and simmer for 10 more minutes until thickened.
For the dumplings: In a bowl, combine the flour, cornmeal, parmesan, baking powder, salt and herbs. Add the melted butter and buttermilk and stir together. Drop the dough using a large serving spoon into the simmering pot, making 6-8 dumplings. Cover with tight fitting lid and cook for about 20-25 minutes without removing lid. Serve immediately by ladling some of the stew into a bowl and topping with a dumpling. Garnish with fresh parsley, a sprinkling of parmesan, salt and freshly ground pepper if desired. Serves 4-6.