Preheat oven to 375°F (190°C). Grease a 9x13-inch baking dish with butter.

Cook bacon until crisp in a skillet. Drain on paper towels, then crumble. Reserve 1–2 tablespoons of bacon fat.

In the same skillet, heat olive oil plus reserved bacon fat over medium. Add onions and a pinch of salt. Cook, stirring occasionally, until golden and soft (about 12–15 minutes). Set aside.

Melt butter in a saucepan over medium heat. Add flour and whisk constantly for 1–2 minutes to cook the raw flour taste (this is your roux).

Gradually whisk in milk in a steady stream. Continue whisking until sauce thickens and coats the back of a spoon, about 6–8 minutes. Season with salt and pepper. Remove from heat.

Arrange a single layer of potato slices on the bottom of the baking dish. Season lightly with salt and pepper. Sprinkle a portion of crumbled bacon, caramelized onions, and a handful of cheese.

Repeat layers until potatoes are used, ending with a generous layer of cheese on top. Pour the warm milk sauce evenly over the layered potatoes — use a spoon to nudge sauce into gaps if needed.

Cover the dish loosely with foil and bake for 40 minutes. Remove foil and continue baking 20–25 minutes until potatoes are tender when pierced and top is golden and bubbly. If the top browns too fast, tent with foil.

Let rest 10–15 minutes before serving so the sauce firms slightly and slices hold better.