Cook turkey bacon in skillet until crisp. Set aside.
Wipe out skillet with a paper towel and melt butter.
Scramble eggs and milk. Pour eggs into hot skillet (med-high heat), and swirl to coat pan evenly. Add salt and pepper to taste. As eggs cook, lift sides and tip pan to move uncooked egg to sides.
Crumble bacon onto omelette, arrange basil on eggs, cover with cheese slices, and fold omelette in half with spatula. After a min. Or two, flip omelette to other side. Cook a minute more. (if calories aren't an issue, you can top with additional cheese)
Add fresh diced tomato and avocado on top after removing from pan.
Serve with sour cream or spicy ranch dressing, if desired. Great with fresh summer fruit!