Preheat your oven to 350”F
Slice the leeks lengthwise then slice it crosswise. Add them to a bowl with cold water. Stir to rinse well and allow them to stay in the water for a few minutes. All the grit and dirt will fall to the bottom of the bowl.
Use your hands and scoop out the leeks from the water and drain them on a kitchen towel.
Preheat a large skillet on medium low flame. Add a lug of olive oil and the leeks with a pinch of sea salt. Saute until wilted and they start to het some color. Adjust seasonings to taste with more sea salt and black pepper. Set aside
Using a mandoline thinly slice the potatoes. Sprinkle all over the top with a good pinch of sea salt and black pepper.
Use your hand and butter a large gratin dish including the sides. (You can use 2 small gratin dishes if you wish)
Layer the thinly slice potatoes on the bottom of the gratin dish overlapping each other. Scoop the sauteed leeks and spread them on top of the potato slices. Sprinkle with the fresh thyme.
In a mixing bowl whisk together the heavy cream with the egg yolk, a dash of nutmeg and the chives. Pour over the leeks. Sprinkle with the grated mushroom jack cheese and cover with aluminum foil.
Bake the leek potato gratin in the preheated oven for about 45 minutes, remove the foil and cook another 10 minutes or so until the cheese is golden on top.