Steam potatoes until still slightly firm. Set aside and let cool. Clean leaks thoroughly, slice and clean again. Use all the way up to the green part as long as it is still tender. Heat 6 tablespoons of unsalted butter and 1/3 cup olive oil together over low heat and cook the leeks till tender and browning. Add 2 tablespoons of brown sugar, sea salt, and 2 tablespoons of apple cider vinegar and continue to cook until bubbling and liquid is evaporated. Remove from heat and let cool.

Whisk eggs with milk, sea salt and white pepper. Butter an oven-safe baking dish (I use a 3-inch-deep 9x9 pan) and layer the bottom with thinly sliced potatoes, parsley, leeks, Gruyere and eggs. Repeat a second time. Keep aside enough Gruyere to sprinkle on the top at the end. Bake at 350° for 40 minutes or until a knife in the center comes out clean