Prep the chicken. Pat the chicken dry with paper towels.
Season both sides with 1 teaspoon salt and 1/2 teaspoon pepper. This helps the chicken brown well and stay juicy.
Heat the pan. Set a large skillet over medium-high heat. Add 1 tablespoon olive oil.
When the oil shimmers, add the chicken in a single layer. Don’t crowd the pan.
Brown the chicken. Sear 4–5 minutes per side until golden. The chicken doesn’t need to be fully cooked yet.
Transfer to a plate and tent loosely with foil.
Cook the mushrooms. Reduce heat to medium. Add the remaining 1 tablespoon oil and the butter. Stir in the mushrooms and a pinch of salt.
Cook 6–8 minutes, stirring occasionally, until they release liquid and turn deep golden.
Add aromatics. Stir in the onion (or shallots). Cook 2–3 minutes until softened. Add the garlic and thyme; cook 30 seconds until fragrant.
Don’t let the garlic burn.
Deglaze the skillet. Pour in the white wine, if using. Scrape up the browned bits with a wooden spoon. Let it simmer 1–2 minutes to reduce by half.
If not using wine, go right in with the broth.
Build the sauce. Add the chicken broth and Dijon. Return the chicken and any juices to the pan. Reduce heat to medium-low, cover, and simmer 5–7 minutes, until the chicken is cooked through (165°F internal).
Add cream. Stir in the cream.
Simmer uncovered 2–3 minutes to thicken slightly. For a thicker sauce, stir in the cornstarch slurry and simmer 1 minute more.
Finish and balance. Squeeze in a little lemon juice, then taste and adjust with salt and pepper. Remove the thyme sprigs if you used fresh.
Serve. Sprinkle with chopped parsley.
Serve with mashed potatoes, buttered noodles, or rice to soak up the sauce.