Preheat the oven to 200°C / 400°F. This temperature is hot enough to brown the top of the gratin and finish the chicken if you choose to oven-finish it while keeping the potatoes creamy.

Prepare the potatoes: Peel (optional) and slice the Yukon Golds 2–3 mm (1/8 inch) thick using a sharp knife or mandoline. Even thickness ensures they cook through at the same rate so the gratin is uniformly tender.

Make the cheesy bechamel for the gratin: In a medium saucepan over medium heat, melt 2 tbsp (28 g) of the butter. Add the thinly sliced onion and half the minced garlic; sauté until translucent and fragrant (about 4–5 minutes). Cooking the aromatics first mellows their sharpness and infuses the milk base with flavor.

Stir in the flour and cook for 1 minute to form a light roux — this removes the raw flour taste and gives the sauce body. Slowly whisk in the milk in a steady stream to avoid lumps, then bring to a gentle simmer. Simmer for 3–4 minutes until the sauce thickens slightly; it will continue to thicken in the oven as it bakes with the potatoes.

Remove from heat and stir in 120 g of the grated cheddar (reserve ~30 g for topping), 1 tsp kosher salt and 1/2 tsp black pepper. Taste and adjust seasoning. The cheese folded into the warm milk creates a glossy, smooth sauce that clings to the potato slices.

Assemble the gratin: Butter a 9 x 13-inch (or similar) baking dish with 1 tsp butter. Layer one-third of the potato slices in a slightly overlapping pattern, sprinkle a pinch of salt and pepper, then pour about one-third of the cheese-milk sauce over the layer. Repeat two more times, finishing with the remaining sauce and the reserved 30 g grated cheddar on top. Layering and seasoning each tier ensures even flavor distribution.

Cover the dish tightly with foil (to trap steam) and bake for 30 minutes. Then remove the foil and bake another 12–15 minutes until the top is golden and the potatoes are tender when pierced with a knife. Baking covered at first prevents drying out; uncovering at the end allows browning and a lacy crisp edge.

While the gratin bakes, season the chicken: Pat the chicken breasts dry (this promotes browning), then season both sides with 1 tsp kosher salt, the remaining 1/2 tsp black pepper, and smoked paprika if using. Let the chicken sit at room temperature for 10 minutes so it cooks more evenly.

Heat a large ovenproof skillet over medium-high heat and add 1 tbsp olive oil and the remaining 2 tbsp (28 g) butter. When the fat is shimmering and the butter foams, add the chicken breasts presentation-side down (smooth side). Sear without moving for 3–4 minutes until a deep golden crust forms — this Maillard browning builds flavor and texture.

Flip the chicken, add the remaining minced garlic and a couple of thyme sprigs to the pan, and baste the chicken with the melted butter and pan juices for 30–60 seconds. Basting coats the meat with flavored fat, promoting even browning and moisture retention.

Transfer the skillet to the oven and roast for 8–12 minutes, depending on breast thickness, until the internal temperature reaches 74°C / 165°F. Oven-finishing cooks the chicken gently through without burning the crust. If your skillet is not ovenproof, move chicken to a rimmed baking sheet.

Remove chicken and let it rest for 5 minutes under loose foil. Resting lets juices redistribute, so when you slice the breast it stays moist. Meanwhile, remove the gratin from the oven and let it sit for 5 minutes — it will settle and be easier to portion.

To serve, spoon a generous portion of cheesy potato gratin onto each plate and top with a whole chicken breast or sliced diagonal cuts. Spoon any buttery pan juices over the chicken and garnish with fresh thyme. The interplay of creamy gratin and savory seared chicken makes a balanced, special-occasion plate.