Whisk the eggs. In a bowl, whisk eggs with milk, salt, pepper, and garlic powder until smooth and slightly frothy. This adds air and makes the eggs lighter.
Warm the pan. Heat a nonstick skillet over medium heat.
Add butter or oil and let it coat the surface.
Scramble the eggs. Pour in the eggs. Let them set for a few seconds, then gently push with a spatula, forming soft curds. Cook until just set and glossy.
Remove from heat; the residual heat finishes them.
Warm the tortillas. Briefly heat each tortilla in a dry skillet or microwave (10–15 seconds) to make them pliable and easier to roll.
Assemble. Lay a tortilla flat. Add a layer of turkey, then spoon on a quarter of the eggs. Sprinkle with cheese and chives.
Roll them up. Fold the sides in slightly, then roll from the bottom up, snug but not too tight to avoid tearing.
Toast the seam. Place the roll-up seam-side down in the skillet over medium heat for 1–2 minutes per side until lightly golden and the cheese melts.
Serve. Slice in half if you like.
Add hot sauce, salsa, or a dollop of sour cream on the side.