Prep the leeks: Slice the leeks thinly, then rinse thoroughly in a bowl of cold water, swishing to remove any grit. Drain well and pat dry. Clean leeks are key to a smooth, grit-free sauce.
Season the chicken: Pat the chicken dry and season both sides generously with salt and pepper. Dry surfaces sear better, which builds flavor.
Sear the chicken: Heat 1 tablespoon olive oil in a large skillet over medium-high.
Add the chicken in a single layer and sear 3–4 minutes per side until golden. Transfer to a plate; it doesn’t need to be fully cooked yet.
Soften the leeks: Reduce heat to medium. Add the remaining 1 tablespoon olive oil and the butter.
Stir in the leeks with a pinch of salt. Cook 6–8 minutes, stirring often, until soft and lightly golden at the edges. If they brown too quickly, lower the heat.
Add aromatics: Stir in the garlic and thyme.
Cook 30–60 seconds until fragrant. Add the Dijon and stir to coat the leeks.
Deglaze: Pour in the wine (if using), scraping up the browned bits. Let it simmer 1–2 minutes to reduce by about half.
Add the chicken broth and bring to a gentle simmer.
Simmer the chicken: Nestle the chicken and any juices back into the pan. Reduce heat to medium-low and cook 6–10 minutes, flipping once, until the chicken is cooked through (internal temperature of 165°F/74°C).
Finish the sauce: Remove the chicken to rest on a plate. Stir in the cream and lemon zest, simmering 2–3 minutes until slightly thickened.
Add lemon juice to taste, plus salt and pepper as needed. The sauce should be silky, not heavy.
Serve: Return the chicken to the pan to coat in the sauce. Top with parsley or chives.
Serve over mashed potatoes, rice, or crusty bread to catch the sauce.