In a medium non-stick skillet, heat 0.5 tsp of olive oil over medium heat.
Add the ground turkey to the skillet and cook until browned and fully cooked through, breaking it into small crumbles.
Stir in the sliced cremini mushrooms and sauté for 3-4 minutes until they are tender and golden. Remove the turkey and mushrooms from the pan and set aside.
In a small bowl, whisk together the whole eggs, egg whites, sea salt, and black pepper until the mixture is uniform and slightly frothy.
Wipe the skillet clean and add the remaining 0.5 tsp of olive oil over medium-low heat.
Pour the egg mixture into the skillet. Use a spatula to gently push the cooked edges toward the center, allowing the raw egg to flow to the edges.
When the eggs are nearly set but still slightly moist on top, spread the mushroom and turkey mixture over one half of the omelette.
Sprinkle the feta cheese over the filling and carefully fold the other half of the omelette over the top.
Cook for another 30 seconds to melt the cheese, then slide the omelette onto a plate and garnish with fresh chives.