Whisk the cornstarch and water together in a bowl until dissolved, then add the eggs and 2 pinches of salt and pepper and whisk until smooth.
Heat a 12-inch nonstick skillet over medium heat for 1–2 minutes, then add the coconut oil or butter and spread to coat the pan.
Pour the egg mixture into the skillet and tilt and swirl the pan so the egg forms a thin, even layer covering the bottom.
Cook until the bottom is set and the top is mostly set but still slightly wet, about 2–3 minutes, lifting and tilting the pan as needed to keep the layer even.
Loosen the edges with a flat spatula and carefully flip the egg wrap to the other side; immediately sprinkle the shredded Swiss cheese evenly over the cooked side.
Continue cooking about 1 minute more until the cheese begins to melt and the top is set, then remove the wrap from the pan.
Layer the turkey slices, tomato, avocado, and spinach over the egg, roll the wrap tightly, cut in half, and serve immediately.
