Heat a few tablespoons of canola oil in a large saute pan over high heat until it begins to smoke.
Season the chicken on both sides with salt and pepper.
Put the chicken in the pan, top side down and cook until golden brown and a crust has formed, about 5 minutes.
Turn the chicken over and continue cooking until the bottom is golden brown and the chicken is cooked through (155 degrees on an instant read thermometer).
Remove chicken to a platter, tent with foil and let rest 5 minutes while making mushrooms.
2. Keep the heat on high and add another tablespoon of canola oil to the pan.
Heat until it begins to shimmer.
Add the mushrooms and thyme, season with salt and pepper, stirring a few times, and cook until the mushrooms are golden brown and their liquid has released and evaporated, about 10 minutes.
Add the chicken stock to deglaze the pan and cook until it is completely reduced.
3. Whisk together the vinegar and mustard until combined.
Slowly whisk in the olive oil and keep whisking until emulsified, season with salt and pepper.
Add the vinaigrette to the mushrooms and cook for 1 minute just to heat through, stir in the parsley and spoon over the chicken.
Use canola or vegetable oil for high heat cooking.
Use extra virgin olive oil to finish a dish or for a vinaigrette.
Do not expose extra virgin olive oil to high heat, as it loses its fresh olive flavor and you pay a lot of money for that flavor.
Also, EVOO does not have a high smoking point.
It will burn at high heat.
Use stainless or nonstick pans because vinegar is in the sauce and acid reacts with cast iron or aluminum pans.
Never wash mushrooms with water or soak them in water to get clean.
Use a brush or a slightly damp cloth or paper towel to wipe them clean.
Remove the stems and reserve for a mushroom stock or to add to a chicken stock.
Most stems on most mushrooms are too tough to eat but still have incredible flavor.
Mushrooms will shrink to about half their size when cooked.
Consider this when preparing portions.
Buy more than you think you need.
To properly sauté, the oil needs to be heated in the pan before adding the mushrooms.
The French translation of "sauté" literally means to "jump" so make sure the oil is jumping hot when the mushrooms are added to the pan.
The only way to get the mushrooms brown and to release their liquid is to have a hot pan.
If not, the mushrooms will literally stew in their own liquid and never brown.
If using a store-bought chicken broth or stock, buy one that says low sodium on the front.
You should be in charge of the amount of salt that is added to any dish.