Still over medium-low heat, melt butter in the 8" skillet, swirling until the bottom of the pan is covered. Whisk together the eggs, milk, salt, and pepper. Pour into the hot skillet. As the bottom of the eggs set, lift up the side of the eggs with a spatula and let uncooked eggs run under the cooked eggs. Continue until egg is fairly well set. Carefully flip the omelette over and sprinkle 1/2 ounce cheese, barley, and 1/2 the asparagus mixture. Turn off heat, fold omelette in half, and allow to sit for 1-2 minutes until cheese melts. Serve with remaining asparagus mixture.
Notes
If you would like to make more than one serving, multiply ingredients by the number of people you would like to serve.