Cook asparagus in water in small saucepan for 3 to 5 minutes until bright green and tender-crisp. Drain. Quickly cool asparagus under cold running water. Drain well and remove to small bowl. Set aside.
Melt butter in same small saucepan on medium-low. Add garlic. Cook for about 1 minute, stirring often, until fragrant.
Add next 5 ingredients. Stir and add asparagus. Heat and stir for about 2 minutes until heated through. Cover to keep warm.
Beat eggs and salt with whisk in small bowl until smooth.
Heat cooking oil in small 8 inch (20 cm) non stick frying pan on medium. Pour egg mixture into frying pan. Stir gently and constantly with spatula for about 1 minute until starting to set. Spread evenly in pan. Cook for about 1 minute until bottom starts to turn golden. Reduce heat to medium low. Scatter asparagus mixture over 1/2 of omelet. Sprinkle cheese over asparagus mixture. Fold other 1/2 of omelette over filling. Cover and cook for about 2 minutes until cheese is melted.
Tip: To roast peppers, place on baking sheet under broiler. Turn peppers frequently until skin is blistered and blackened. Transfer to bowl and cover with plastic wrap. Let sweat for about 15 minutes until cool enough to handle. Peel and discard skins. Or you can purchase roasted red peppers in a jar at most grocery stores. Drain peppers on paper towel before using.