Heat 1 Tbsp avocado oil in a large skillet over medium-high heat.
Add the chopped chicken thighs and let them sear undisturbed for a few minutes until they begin to brown.
Stir occasionally and continue cooking until most liquid has evaporated and the chicken is browned, about 5–8 minutes.
Stir the 1/3 cup pesto into the chicken until evenly coated, then add the baby spinach and cook, stirring, until wilted, about 2–3 minutes.
Taste the chicken mixture and add sea salt to taste.
Heat 2 to 3 tsp avocado oil (or spray) in a small 6-inch skillet over medium heat.
Whisk 2 or 3 eggs in a bowl with a pinch of sea salt until blended.
Pour the beaten eggs into the hot small skillet and cook until the edges firm and the center begins to set, about 2–3 minutes.
Carefully flip the omelette and cook an additional 30 seconds to 1 minute, until done to your liking, then transfer to a plate.
Fill the omelette with the pesto chicken and wilted spinach mixture, then sprinkle with crumbled feta and additional pesto if desired.