Very lightly dredge chicken parts (seasoned with salt, pepper, a bit of paprika and if you like a bit of celery salt) in flour.
Heat olive oil and butter in a sauté pan over medium high heat.
Brown chicken quickly on all sides and remove.
Add garlic, onion, pepper, shallot, and sauté over medium heat until everything is limp and reduced. Do not brown!
Add mushrooms, stir all of this together, and when it is all about the same consistency turn up heat to high
Add white wine and reduce by half.
Add chicken stock, and fresh rosemary, and salt and pepper to taste.
Squeeze in juice of ½ lemon. (you may add a couple of tsp. of lemon zest if you like)
Place chicken in casserole on one layer, and pour sauce all over top of chicken.
Cover with foil and bake at 375º F for about 45 minutes.
Turn heat up to 425º F, uncover and bake to reduce sauce, and slightly brown chicken.
You can serve it this way, or if you want to do a fancy prep, you can remove the chicken and deglaze again, and finish with a bit of butter, or even put all into a blender and make a smooth sauce. I have even added cream, which is rich, but very tasty. If you just serve it out of the oven as is, its rustic and has a nice texture.
Now what is this? It's sort of pan roasting, and its sort of braising, and its almost a fricassee, but it isn't quite any of them!