Preheat oven to 350℉ / 325℉ (convection) / 170℃ (fan-forced).
Grease a deep 2-litre/2-quart ceramic baking dish thoroughly completely with extra butter, setting it aside cleanly on your workspace workspace.
Sauté sliced leeks, minced garlic, and thyme in the butter for 6–8 minutes until soft and translucent, removing from heat.
Whisk thickened cream, milk, nutmeg, ½ cup Cheddar cheese, half the Parmesan, salt, and pepper together in a large jug.
Layer one-third of thinly sliced potatoes in the prepared dish, topping with half the sautéed leek mixture evenly to cover.
Repeat with another layer of potatoes and remaining leeks, finishing with a neat layer of overlapping potato slices on top.
Pour the cream mixture slowly over the potato stack, pressing gently so the liquid settles into every crevice cleanly.
Scatter remaining Cheddar, remaining Parmesan, and fresh chives over the top to form a decorative crown.
Bake, covered with foil, for 45 minutes, remove foil, and bake uncovered for 20–25 minutes until golden-brown.