Prepare the chicken: Pat the thighs very dry with paper towels — dryness is the key to a golden, crisp skin. Season both sides with 1 1/2 tsp kosher salt and 1 tsp freshly ground black pepper. Lightly dust both sides with the 2 tbsp all-purpose flour and shake off excess; the flour helps promote browning and will also slightly thicken the braising liquid.

Brown the chicken: In a large heavy skillet or Dutch oven, heat 1 tbsp olive oil and 2 tbsp (28 g) of butter over medium-high heat until the butter foams and just begins to color. Add the thighs skin-side down, gently pressing so the skin contacts the pan evenly. Sear without moving 5–7 minutes until deeply golden — this Maillard crust locks in flavor and gives the finished dish contrast. Flip and sear the other side 3 minutes. Transfer chicken to a plate.

Sweat the aromatics: Reduce heat to medium. Add the sliced shallots to the pan and cook 3–4 minutes until soft and translucent — sweating (not browning) draws sweetness and builds the base for the sauce. Add the minced garlic and cook 30–45 seconds until fragrant; garlic cooks quickly and can turn bitter if overcooked.

Deglaze with wine: Pour in the 1 cup dry white wine to deglaze the pan, scraping up any browned bits from the bottom (those are concentrated flavor). Let the wine simmer briskly 3–4 minutes to reduce by about a third — this concentrates the wine flavors and burns off some alcohol, leaving a clean acidity that will brighten the sauce.

Build the braise: Add 1 cup low-sodium chicken stock, the fresh thyme sprigs, and the seared chicken (skin-side up) back to the pan. Bring to a gentle simmer, then reduce heat to low, cover partially, and cook 20–25 minutes, or until the internal temperature of the thighs reaches 75–80°C (165–175°F) and the meat is tender. Braising at a low simmer ensures the meat becomes tender while preserving the crispy skin on top.

Finish the sauce: Remove the chicken to a warm plate and tent with foil. Discard the thyme sprigs. Increase the heat to medium-high and reduce the braising liquid 3–5 minutes if it’s thin. Turn off the heat and whisk in the remaining 4 tbsp (56 g) cold butter, one piece at a time, to emulsify and thicken the sauce — this technique (monter au beurre) gives the sauce a glossy, velvety finish. Stir in 1 tbsp fresh lemon juice and adjust seasoning with salt and pepper to taste.

Rest the chicken briefly: Return the chicken to the pan skin-side up for 1–2 minutes to rewarm and re-crisp slightly in the residual heat of the sauce, then plate and spoon sauce over the top. Resting allows juices to redistribute so the meat stays moist.

Prepare the buttered asparagus while the chicken braises: Trim asparagus (snap the woody ends off or cut 2–3 cm from the bottom) so you have even stems for uniform cooking. Bring a medium pot of salted water to a rolling boil — boiling briefly before sautéing speeds cooking and gives a bright green color.

Blanch the asparagus 1–2 minutes (depending on thickness) until just tender and bright green, then immediately plunge into an ice bath or run under cold water to stop cooking and preserve color and texture. Blanching evens cooking and prevents overcooked, limp asparagus.

Sauté the asparagus: In a medium skillet over medium heat, melt 2 tbsp butter. Add the drained asparagus and sauté 2–3 minutes until glossy and heated through; finish with 1/2 tsp salt, freshly ground black pepper, and 1/2 tsp lemon zest if using. Toss with 1 tbsp chopped parsley before serving. The butter and lemon brighten and coat the spears without overwhelming their fresh flavor.

Plate and serve: Spoon a little of the wine-butter sauce onto warm plates, place a chicken thigh on each, then arrange a bundle of buttered asparagus alongside. Sprinkle with remaining chopped parsley and an extra twist of black pepper. Serve immediately so the sauce is silky and the chicken skin stays crisp.