In a mixing bowl, whisk together 1/2 tsp cornstarch and 1 tsp water until smooth, then add 2 large eggs and 2 pinches of salt and pepper; whisk until well combined.
Heat a 12-inch nonstick skillet over medium heat for 1–2 minutes, then add 1/2 Tbsp 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 eggs form an even, thin layer covering the bottom.
Cook about 2–3 minutes, lifting and tilting the pan as needed, until the bottom is set and the top is mostly set but still slightly wet.
Loosen the edges with a flat spatula, slide the spatula fully under the egg, and carefully flip the wrap to the other side.
Immediately sprinkle 1/3 cup finely shredded Swiss cheese evenly over the cooked surface and continue to cook about 1 minute until the cheese melts and the top is set.
Remove the egg wrap from the pan and layer 4 thin slices deli turkey, the thinly sliced small tomato, 1/2 sliced avocado, and 1/2 cup spinach down the center.
Roll the wrap tightly, cut in half if desired, and serve immediately.