Preheat and prep: Preheat oven to 400°F (200°C). Butter or oil a 9x13-inch (or similar) gratin/baking dish. Preheating ensures the baking time and browning are consistent from the start.

Cook the rice: Rinse 1 cup uncooked long-grain white rice under cold water until the water runs clear (this removes surface starch so grains stay separate). Cook the rice in 1 3/4 cups water with a pinch of salt: bring to a boil, reduce to low, cover and simmer 15 minutes, then rest 5 minutes off heat. Fluffy rice provides a cushion in the gratin and absorbs the sauce without becoming gluey.

Season and cook the chicken: Pat the 1 lb chicken breasts dry and season with salt and pepper. Heat 1 tbsp olive oil in a skillet over medium-high heat. Sear the breasts 3–4 minutes per side until golden (they will not be fully cooked through). Searing develops Maillard flavor — deeper savory notes — which carry through the casserole. Transfer to a plate and reserve.

Sweat the aromatics: In the same skillet reduce heat to medium, add 1 tbsp butter and the diced onion. Cook 4–5 minutes until soft and just starting to color, then add the minced garlic and cook 30 seconds until fragrant. Sweating the onion first softens its bite and releases sugars that add sweetness and depth to the sauce.

Make the béchamel-style cheese sauce: Sprinkle 2 tbsp flour into the skillet with the softened onion and cook 1–2 minutes while stirring to toast the flour—this removes raw flour taste. Slowly whisk in 1 cup chicken stock and 2 cups whole milk until smooth and bring to a gentle simmer. Simmer 3–4 minutes to thicken. The roux (butter + flour) thickens the sauce and the low simmer prevents scorching while building body.

Finish the sauce: Lower heat to medium-low, remove from heat and stir in 1 cup (about 113 g) of the shredded cheddar until melted and smooth. Add the dried thyme, and taste for seasoning (add salt and pepper). Stirring off heat prevents the cheese from becoming grainy; using part of the cheese in the sauce gives luscious creaminess and helps the casserole bind.

Shred the chicken and combine: While the sauce is warming, transfer the seared chicken breasts to a small pot, add 1/4 cup water (or a splash of stock), cover and simmer over low heat 8–10 minutes until cooked through (internal temp 165°F / 74°C). Let rest 5 minutes, then shred into bite-sized pieces. Cooking just to temperature keeps the chicken tender; shredding disperses meat evenly through the gratin.

Prepare the potatoes: Thinly slice the Yukon Gold potatoes (about 1/8 inch / 3 mm thick) — a mandoline makes this quick and even. To prevent undercooked potatoes in the finished gratin, parboil the slices 4 minutes in salted boiling water, then drain and pat dry. Parboiling starts their cook so the final baking time achieves tender, not raw, potatoes.

Assemble the gratin: In the prepared baking dish, spread the cooked rice into an even layer (this base soaks up sauce). Scatter the shredded chicken evenly over the rice, then pour the warm cheese sauce over, gently mixing to distribute. Arrange half the potato slices in a single layer across the top, slightly overlapping. Sprinkle with remaining 1/2 cup shredded cheddar. Layering in this order ensures rice absorbs sauce, chicken stays moist, and potatoes form a creamy top layer.

Add the crunchy topping: In a small skillet, melt the remaining 1 tbsp butter, stir in 1/4 cup panko breadcrumbs and toast 2–3 minutes until golden. Sprinkle the warm crumbs over the cheese layer. Toasting panko in butter crisps it and adds a nutty flavor and a stable crunchy finish that resists sogginess.

Bake: Cover the dish loosely with foil and bake at 400°F (200°C) for 20 minutes, then remove foil and bake another 20–25 minutes until bubbly and the top is golden and the potatoes are tender when pierced with a knife. Covering initially steams and heats the interior without over-browning; finishing uncovered develops color and texture.

Rest and serve: Let the gratin rest 10 minutes before serving to allow the sauce to thicken and settle (this makes cleaner slices). Garnish with a grind of black pepper or chopped parsley if desired. Resting improves texture and makes serving neater.