Preheat your oven to 180°C (350°F). Grease a 9-inch baking dish with a little butter to prevent sticking.
Using a mandoline or sharp knife, thinly slice the peeled russet potatoes into even rounds, about 1/8 inch thick. Arrange the slices in a bowl of water to prevent browning.
Melt 2 tablespoons of butter in a medium saucepan over medium heat, until it starts to foam softly and smell buttery.
Add the minced garlic to the melting butter and cook for about 30 seconds until fragrant, with a gentle sizzle filling the air.
Stir in the all-purpose flour and cook for another minute, whisking constantly until the mixture turns a light golden color and thickens slightly.
Gradually pour in the milk, whisking continuously to create a smooth sauce. Bring it to a gentle simmer for 2-3 minutes until it thickens enough to coat the back of a spoon.
Stir in the grated cheddar cheese until melted and the sauce becomes creamy and smooth. Add a pinch of smoked paprika for color and aroma, if using.
Arrange a layer of potato slices in the prepared baking dish, overlapping slightly to cover the bottom.
Pour a portion of the cheese sauce over the layer, ensuring each slice is coated and the dish starts to look creamy.
Repeat layering with remaining potato slices and cheese sauce, finishing with a top layer of sauce and a sprinkle of extra cheese for a gooey finish.
Cover the dish with aluminum foil and bake for 45 minutes until the potatoes are tender and the sauce is bubbling.
Remove the foil and bake for an additional 15 minutes, until the top is golden and crispy with bubbly edges.
Let the dish rest for a few minutes out of the oven, then serve warm, enjoying the creamy, cheesy layers with a crispy top.
