Preheat your oven to 400°F (200°C) and generously grease a 2-quart casserole dish with butter to prevent sticking.

Arrange half of the potato slices evenly across the base of the prepared dish, forming a single layer. Sprinkle lightly with salt and freshly ground black pepper. Follow by layering the onion rings evenly over the potatoes. Top with the remaining potato slices, then season once again with salt and pepper to taste.

In a medium-sized saucepan, melt the butter over medium heat. Once fully melted, whisk in the flour and ½ teaspoon salt. Continue whisking constantly and cook for about 1 minute, allowing the flour to lose its raw flavor and form a smooth roux.

Begin slowly adding the milk, about ¼ cup at a time, whisking thoroughly after each addition. This gradual process ensures a smooth, lump-free sauce. Continue cooking and whisking until the mixture thickens to a velvety consistency—this should take approximately 3 to 5 minutes.

Add the shredded Cheddar cheese all at once and stir continuously until the cheese has fully melted and the sauce is smooth and glossy, about 30 to 60 seconds.

Carefully pour the rich cheese sauce over the layered potatoes and onions, ensuring it seeps through evenly. Cover the dish tightly with aluminum foil.

Bake in the preheated oven for approximately 1 hour and 30 minutes, or until the potatoes are fork-tender and the cheese sauce is bubbling around the edges.

Let the gratin rest for a few minutes before serving to allow the sauce to settle.