Preheat oven to 350 degrees.
Peel the potato and thinly slice. I used a mandoline to slice the potato as thin as for chips/crisps. I bought mine in a Japanese grocery store in downtown LA, but you can buy the New Benriner Vegetable Cutter online. Put the sliced potatoes in bowl and cover them with cold water.
Slice the onion and saute in olive oil until soft and translucent.
Butter the baking dish and lay down an overlapping layer of potato slices on the bottom of the dish (you will use about half the potatoes). Spread out the layer of cooked onions and then the prosciutto. Put down a layer of arugula and top with crumbled goat cheese and thyme.
Whisk together the egg and milk and gently pour over the layers in the pan. Top with the remaining slices of potato and sprinkle fresh thyme on top.
Cover with foil and put in 350-degree oven. Bake for about 30 min before removing the foil. The frittata is done when the eggs are set. I wanted it to be a little browner on top, so for the last 5 minutes, I brushed the top with melted butter and put it under the broiler.