Preheat your oven to 180°C (356°F). Lightly butter a 9x13 inch baking dish to prevent sticking.
Using a mandoline, slice the potatoes as thin as paper, about 2 mm thick. Keep the slices in a bowl of cold water to prevent browning.
In a saucepan over medium heat, melt the butter and add the minced garlic. Cook until fragrant, about 1 minute, until you can smell the garlic and butter sizzling gently.
Pour in the heavy cream, then add salt and black pepper. Bring the mixture to a gentle simmer, stirring occasionally.
Stir in the shredded cheddar cheese until the sauce becomes smooth and velvety, about 2 minutes. Remove from heat and set aside.
Drain the potato slices and pat them dry with a clean towel to remove excess water.
Layer the potato slices in the prepared baking dish, overlapping slightly to create a uniform layer.
Pour a third of the cheese sauce over the layered potatoes, spreading evenly with a spatula.
Repeat layering potatoes and pouring sauce until all ingredients are used, finishing with a generous layer of sauce on top.
Sprinkle the extra shredded cheese evenly over the top for a bubbly, golden crust.
Place the dish in the oven and bake for 45-50 minutes, until bubbling and golden brown on top.
Remove from the oven, let rest for 10 minutes to set, then slice and serve hot. The potatoes should be tender inside with a crispy, cheesy crust on top.
