1. Heat a skillet over low heat. Add butter and melt. When butter is bubbly, add eggs, along with salt and pepper to taste.
2. Using a heatproof rubber spatula, push outer edge of eggs toward center of pan, then tilt skillet to distribute eggs. Continue this way until eggs have nearly set, which should only take a couple of minutes.
3. Add pea shoots, peas, goat cheese, chives, and thyme to center of eggs. Turn off heat, cover, and leave for 2 minutes.
4. To serve, fold half of omelet over filling and slide onto a plate. Garnish with pea shoots, peas, and chives.