Peel the potatoes and slice them into 1/8-inch rounds—I recommend using a mandoline slicer for consistency, which ensures even cooking throughout the dish. Place the sliced potatoes in a bowl of cold water to prevent browning while you prepare the other components. Preheat your oven to 350°F and lightly butter a 9x13-inch baking dish (or similar size casserole).

While the oven preheats, prepare your leeks by trimming the dark green tops and roots, then slicing them into thin half-moons, using only the white and light green parts. Mince the garlic cloves finely. Measure out your thyme. This mise en place ensures everything is ready when you start cooking the sauce.

Melt the remaining 2 tablespoons of butter in a large saucepan over medium heat. Add the sliced leeks and cook for about 2 minutes, stirring occasionally, until they begin to soften. Add the minced garlic and thyme, cooking for just 30 seconds until fragrant—this short cooking time prevents the garlic from becoming bitter while releasing its flavor into the butter.

Pour in the milk and heavy cream, stirring to combine with the leek mixture. Add the salt, pepper, and nutmeg. Bring the mixture to a boil over medium-high heat, then reduce the heat to medium-low and simmer for about 5 minutes, stirring occasionally, until the sauce thickens slightly—it should coat the back of a spoon. I find that letting it simmer allows the flavors to meld beautifully and the sauce to develop the right consistency for coating the potatoes.

Drain the potatoes from their cold water bath and pat them dry with paper towels—this step is important because excess moisture can make the dish watery. Add the drained potatoes to the hot cream sauce, stirring gently to coat all the slices evenly. Transfer the potato and leek mixture to the prepared baking dish, spreading it into an even layer. Bake uncovered at 350°F for approximately 1 hour, until the potatoes are completely tender when pierced with a fork and the top is lightly golden.