Peel the potato and thinly slice. I used a mandoline to slice the potato as thin as for chips/crisps. Put the sliced potatoes in bowl and cover them with cold water to keep them from turning brown.
Slice the onion and saute in olive oil until soft and translucent.
Butter a 9x12 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 half of the 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 more brown on top, so for the last 5 minutes, I brushed the top with melted butter and put it under the broiler.