Slice the potatoes in half using a mandoline (if you have one); otherwise slice them very thinly.
Chop off the end of the leek, slice in half lengthways and wash well between the layers. Then chop into 1 cm (1⁄2 in) chunks, including the green part.
Add the cream, mustard, thyme leaves, and salt and pepper to a bowl and mix well. Set aside.
Grease the inside of a shallow rectangular oven dish with the butter. Grate the garlic into the dish, spreading it around evenly and mixing into the butter. This will give a lovely garlicky hint to the whole dish.
Using half of the potatoes, fill the base of the dish with layers of both types of potatoes, then add a middle layer of all the leeks and use the remaining potatoes to form the top layer. Make sure you push the top layer down well as the leeks may be a bit springy.
Pour the cream mixture evenly over the top, making sure everything is covered well.
Pop into the oven for 1 hour until lovely and crispy on top.
Use larger potatoes rather than smaller ones so you spend less time peeling.