Add olive oil to a hot Dutch Oven. Brown the chicken pieces (I used 2 drums and 2 thighs, bone-in.)
While the chicken is browning, dice your turnips (or potatoes) into bite sized pieces. Cut your onion into slices, then in half. Crush your garlic.
Once the chicken is brown, remove from pan. Add the onions, garlic and turnips. Allow to cook for about 5 minutes, stirring occasionally.
Once the onions have started to soften, put the chicken pieces on top of the vegetables. Sprinkle with 3 teaspoons of herbs de provence. Add a bit more salt and pepper at this point. Slowly add 2 1/2 cups or so of chicken stock. You just want to cover the vegetables. Bring to a gentle boil, then reduce heat to a simmer. Cover and let simmer for 45 minutes.
While that is simmering, clean and half or quarter the mushrooms. After 45 minutes, add the mushrooms, replace the lid and simmer for another 15 minutes.