The chicken is from a recipe in America's Test Kitchen Family Cookbook. I changed a few things here and there...You can use boneless skinless chicken breast as well, but I like the full flavor you get from the whole chicken.
Adjust oven rack to the middle position and heat the oven to 375°F.
Spread flour in a shallow dish. rinse chicken breasts, pat dry and season with salt and pepper. Dredge in flour to coat shaking off any excess flour.
Heat 2 tablespoons of the oil in a large dutch oven over medium-high heat until just smoking. Add the chicken skin side down and cook until light golden brown. Flip pieces and cook on all sides to the same consistency, about 10 minutes total. Remove from pan and keep warm.
Add a little more of the oil to the pan on high heat and add the bacon, mushrooms, garlic and onions. Season with salt/peper and cook just long enough to crisp up the bacon and get some color on the mushrooms, about 2 to 3 minute Stir in the tomato paste and rosemary/thyme and cook about 1 minute longer. Place the chicken pieces back into the pan skin-side up and spread them out evenly, pushing them down into the mushrooms and onions. Add the Marsala, scraping up the brown bits from the bottom of the pan, and add the chicken broth. Cover and place the whole pot in the oven and cook until the tops of the chicken are golden brown, 30 to 35 minutes.
In the mean time, cook your polenta.
CHEESY HERB POLENTA: Bring the chicken stock, half and half and salt to a boil in a large, heavy-bottomed pot.
Pour the polenta into the boiling mixture in a slow stream while whisking constantly in a circular motion. Bring to a simmer, still stirring constantly.
Reduce heat to low and cook, stirring vigorously and scraping the sides and bottom of the pot; until the polenta becomes soft and smooth, about 30 minutes.
Stir in the herbs, butter and the cheese, ¼ cup at a time, until thick and creamy.
Season to taste with salt and pepper.
Use tongs to remove the chicken from the pan and transfer onto a serving platter and keep warm.
Set the dutch oven back over the burner on high heat. Bring up to a boil and cook until thickened and flavors have become concentrated, about 3 to 4 minute.
Shut off the heat, add the butter cubes and stir gently to melt the butter evenly. This will make the sauce silky smooth and give it a richer taste. Taste and season with salt and pepper. Add the lemon juice and fold in the parsley.
To Serve:Ladle Polenta onto serving plates. Arrange one chicken quarter atop each mound of polenta.Spoon the sauce and mushrooms over the chicken. Garnish with fresh parsley or a spring of rosemary.