Preheat oven to 375 degrees F.

In a small bowl, toss together both cheeses, potato starch or cornstarch, salt and black pepper. Set aside.

Pour 1 tablespoon of the melted butter into the bottom of a 9-inch cast iron skillet, and swirl it around to evenly coat the bottom and sides. Arrange the potatoes in overlapping concentric circles in a single layer at the bottom of the pan. This will use approximately a quarter of your sliced potatoes. Drizzle with 1 teaspoon of butter and sprinkle with 2 tablespoons of the cheese-pepper mixture. Repeat four times, or until the potatoes are used up; you should have about 1 tablespoon of the mixture left over; reserve this.

Lightly coat a sheet of foil with nonstick spray and tightly cover the pan. Bake for 35 minutes. Using pot holders, firmly press onto the foil to compact the potatoes a bit. Remove and reserve the foil, and bake for another 25 to 30 minutes, until lightly brown all over. Remove from the oven and press down again with the reserved foil. Place under the broiler briefly, until evenly golden brown on top.

While the galette bakes, toss together the arugula with the oil and vinegar and season lightly with salt and pepper.

Once the galette is out of the oven, let it rest in the skillet for a few minutes before running a knife around to ensure that it is loose. Gently tip the skillet over your sink to drain any excess butter or oil. Invert it onto a plate or cutting board, then flip right side up. Cut the galette into wedges, then top with the dressed greens, and sprinkle with the reserved cheese-pepper mixture. Enjoy!