Preheat and prep: Preheat the oven to 375°F (190°C). Lightly butter a 9x13-inch (or similar) baking dish and set aside. Preheating ensures the gratin begins cooking immediately when it hits the oven so the milk emulsion doesn’t separate.

Slice the potatoes very thinly: Using a sharp knife or mandoline, slice the potatoes 2–3 mm thick and place them in a large bowl of cold water while you work. Thin, even slices cook uniformly and release starch into the water—rinsing reduces excess surface starch, which helps the layers remain creamy rather than gluey.

Make the garlicky white sauce (light béchamel): In a medium saucepan over medium heat, melt 4 tbsp butter. Add the finely diced onion and sauté 4–5 minutes until soft and translucent—this gives a gentle sweet base without browning. Add the minced garlic and cook 30 seconds until fragrant (don’t let it brown or it will turn bitter). Sprinkle the flour over the butter/onion and whisk continuously for 1 minute to cook the raw flour taste and form a blond roux, which will thicken the milk into a silky sauce.

Slowly add milk while whisking to prevent lumps: Gradually pour in the 2 cups of milk while whisking vigorously. Bring the mixture to a gentle simmer (do not boil) and cook for 3–4 minutes until slightly thickened. Season with 1 tsp black pepper, 1 tsp salt, 1 tsp thyme, and 1/2 tsp smoked paprika. The gentle simmer cooks out the floury taste and concentrates the milk, producing a creamier mouthfeel without heavy cream.

Assemble the gratin: Drain the potatoes and pat dry. Arrange a single, slightly overlapping layer of potato slices in the prepared dish. Spoon enough white sauce to lightly coat the layer (about 1/3–1/2 cup). Sprinkle about 1/3 of the shredded cheddar evenly and repeat two more times to create 2–3 layers. Finish with the remaining sauce and a light sprinkle of cheese on top. Layering with sauce between slices promotes even cooking and prevents dry centers.

Bake the gratin: Cover the dish tightly with foil and bake for 35 minutes. Then remove the foil and bake another 15–20 minutes until the top is bubbling and the cheese edges turn golden brown. Tent for 10 minutes before serving. Covering at first traps steam and finishes cooking the potatoes; removing foil late allows Maillard browning and crisp cheese edges.

Prepare the chicken (salt in advance): Pat the chicken breasts dry and season both sides with 1 tsp kosher salt and 1/2 tsp black pepper. If you have time, salt the breasts 20–30 minutes ahead—this brief dry-brine seasons through and improves moisture retention.

Butter-baste and sear the chicken: In a large skillet over medium-high heat, warm 2 tbsp olive oil until shimmering. Add the chicken breasts and sear 4–5 minutes without moving until a golden crust forms; flip and add 2 tbsp butter and 2 minced garlic cloves. Reduce heat to medium and baste (spoon the butter over the breasts) while cooking another 4–5 minutes until the internal temperature reaches 160°F (71°C). The initial high heat creates a flavorful crust that locks juices; finishing with butter and garlic adds gloss and deep garlic flavor—remove at 160°F because carryover will bring it to a safe 165°F while resting.

Rest the chicken: Transfer the chicken to a cutting board and let rest 6–8 minutes to let juices redistribute; slice on a slight bias just before plating. Resting avoids spurting juices on the plate and gives a juicier bite.

Plate and finish: Spoon a generous portion of potato gratin onto each plate; top with a butter-basted chicken breast and spoon any pan juices over the chicken. Garnish with a small sprinkle of fresh thyme or chopped parsley if desired. The hot gratin under the chicken keeps the chicken warm and the pan juices finish the dish with extra flavor.