Prep the chicken: Pat chicken dry and season both sides with 1 teaspoon salt and 1/2 teaspoon pepper.
If the breasts are thick, slice them horizontally into cutlets for quicker, more even cooking.
Sear the chicken: Heat olive oil and butter in a large skillet over medium-high heat. Add the chicken in a single layer and sear until golden, about 3–4 minutes per side, depending on thickness. Transfer to a plate; it’s fine if the chicken is slightly underdone at this point.
Sauté aromatics: Reduce heat to medium.
Add the chopped shallot and cook 1–2 minutes until translucent. Stir in garlic and cook 30 seconds, just until fragrant. If using mushrooms, add them now and cook until lightly browned and their moisture evaporates.
Deglaze and build the base: Pour in the chicken broth and use a wooden spoon to scrape up the browned bits.
Let it simmer 2–3 minutes to reduce slightly.
Stir in Dijon and cream: Whisk in the Dijon mustard until smooth, then add the cream. Bring to a gentle simmer. The sauce should thicken a touch and look glossy.
Return the chicken: Add the chicken and any juices back to the skillet.
Spoon sauce over the top. Simmer on low for 3–5 minutes, or until the chicken is cooked through (internal temp 165°F/74°C) and the sauce clings to a spoon.
Finish and balance: Stir in lemon juice and most of the herbs. Taste and adjust with salt, pepper, or a little extra Dijon if you want more tang.
If using spinach or sun-dried tomatoes, fold them in now until just warmed and wilted.
Serve: Sprinkle remaining herbs on top. Serve hot with rice, mashed potatoes, pasta, or crusty bread to catch the sauce.