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 turn up the heat to high when it is all about the same consistency.
Add white wine and reduce by half.
Add chicken stock, fresh rosemary, and salt and pepper to taste.
Squeeze in the juice of ½ lemon. (you may add a couple of tsp. of lemon zest if you like)
Place chicken in a casserole on one layer, and pour the sauce all over the top of the chicken.
Cover with foil and bake at 375º F for about 45 minutes.
Turn the heat 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 it all into a blender and make a smooth sauce. I have even added cream, which is rich but very tasty. If you serve it out of the oven as is, it's rustic and has a nice texture.