Prep the chicken. Pat chicken dry and season both sides with salt and pepper. If using large breasts, pound to an even thickness so they cook uniformly.

Brown the chicken. Heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium-high. Sear chicken 4–5 minutes per side until golden. Transfer to a plate; it will finish cooking in the sauce.

Soften aromatics. Lower heat to medium. Add remaining 1 tablespoon butter. Sauté shallots for 2–3 minutes until translucent. Add garlic and cook 30 seconds until fragrant. Don’t let them brown.

Deglaze. Pour in white wine. Scrape up browned bits from the pan with a wooden spoon. Let it simmer 2–3 minutes to reduce by half. If skipping wine, use chicken stock and a squeeze of lemon later.

Build the sauce. Stir in 1/2 cup chicken stock, heavy cream, and Dijon. Whisk until smooth. Simmer gently 3–4 minutes until slightly thickened. If too thick, add a splash more stock.

Season and add tarragon. Stir in chopped tarragon and a pinch of salt and pepper. Taste and adjust. Add a light zesting of lemon and a small squeeze of juice to brighten.

Finish the chicken. Return chicken and any juices to the pan. Simmer on low 4–6 minutes, turning once, until cooked through and the sauce coats the chicken. Aim for 165°F internal temperature.

Garnish and serve. Sprinkle with more tarragon. Serve hot over mashed potatoes, buttered noodles, rice, or with crusty bread and a green side.