Break the 5 eggs into a bowl and add in the milk. Whisk with anticipation (and vigor:)) until the eggs become slightly stiff.
Warm up 1 tablespoon of the oil in a medium skillet over medium heat. Once hot, add in the leek and sauté until wilted, about 5 minutes.
Give the eggs another few stirs, and add the extra teaspoon of oil to the pan. Then, tilt the pan creating a little puddle of oil in one corner. Pour the eggs into the oil and slowly level off the pan setting it back on the hot stove.
Let the eggs cook slowly over medium heat. Once the edges start to settle, take a wooden spoon and gently push the edges toward the middle letting the uncooked eggs move out towards the edge to cook. Do this just a few times until the eggs are almost done.
Sprinkle with goat cheese and avocado. Serve with thick toast.
You may skip the leek or substitute 1/4 cup chopped onion or a average sized shallot, chopped.