In a small bowl lightly whisk the eggs, milk, and spice blend with a fork until frothy. Heat a 9- or 10-inch skillet with sloped sides on high. Add the oil to the pan and tilt it to coat the bottom. Then add the butter and swirl it around the pan.
Once the butter has melted and stopped sizzling, pour the eggs into the pan. Tilt the pan with your other hand to spread the egg evenly, for about 45 to 60 seconds.
When the egg is mostly set (the bottom should be cooked but not browned), shake the pan to loosen the eggs, then add the Parmesan and asparagus to one half of the omelet, reserving some for garnish. Tilt the skillet and, using the tip of the spatula, pull the omelet away from the opposite edge of the pan. Fold the omelet in half, then slide it onto a plate. Garnish the omelet with additional Parmesan cheese, asparagus, and the spice blend, and serve immediately.