Add softened cream cheese, chives, dill, and onion powder to small bowl. Use fork to mash ingredients together until well incorporated. Set aside.
Crack eggs directly into second small bowl. Add milk, salt, and pepper to bowl, then whisk ingredients together until fully combined. Mixture should be pale in color and no longer streaky. Set eggs aside.
Heat skillet over medium heat. When pan is warm, add neutral oil and swirl pan to distribute oil across surface. Continue heating skillet until oil is hot and shimmery.
When oil is hot, pour egg mixture into skillet slowly. Tilt and swirly skillet to spread egg mixture into one even layer, completely covering bottom of skillet. Cook eggs 3 minutes or until eggs are set and no longer runny, but still slightly shiny.
Working quickly, place smoked salmon on half of omelette. Top salmon with capers (optional) and dollops of cream cheese mixture.
Run silicone spatula under edge of omelette to loosen from pan, then carefully lift edge closest to plain half of omelette. Fold plain half of omelette over to cover filling and press gently on top of omelette with spatula to make halves stick.
Slide omelette out of skillet and onto serving plate. Serve immediately with desired sides.
Recipe Notes
Make it Dairy Free: Use non-dairy milk and plant-based cream cheese.