In a medium bowl, whisk the eggs until light and frothy. Add the shoestring potatoes and let sit for a few minutes while you heat the skillet.
Preheat the broiler (set it to medium if you have the option). Heat a No.8 Field Skillet over medium heat for a couple of minutes. Add the olive oil and heat until shimmering. Pour the egg mixture into the skillet and stir a couple of times to distribute the potatoes. Cook, occasionally pushing the potatoes down gently, until the bottom and sides of the skillet are set and golden brown, 4 to 5 minutes.
Transfer the skillet to the oven and broil until the top of the tortilla is just set. Remove from the oven and invert a plate on top of the skillet. Carefully flip the tortilla over onto the plate. Let cool slightly, then cut into wedges and serve.
