In a blender or food processor, add first 4 ingredients, and about half the olive oil. Blend for about 30 seconds, then drizzle remaining oil into blending while blending. Slowly add the coconut milk until at desired creaminess and consistency. Set aside.
Heat a skillet over medium heat, add a little butter or coconut oil. Pour egg mixture into pan, and let it sit and cook for about 3-4 minutes. Add the turkey, basil, parsley, salt and pepper on top of the egg. Using a spatula, gently fold on side over on top of the other half. Let cook for another couple minutes.
In a small bowl, gently toss the tomato, avocado and 2 tablespoons of pesto sauce.
Remove omelette from heat. Slide onto a plate and top with tomato, avocado, pesto mixture. Enjoy!