Heat the oil over medium high heat in an 8 inch, oven safe skillet. (I used a seasoned cast iron skillet to avoid any problem with sticking.)
In a small bowl, beat the eggs, salt and pepper. Set aside. Preheat broiler to high.
Add the garlic, chard and mushrooms to the skillet. Saute 2-3 minutes, until the vegetables begin to soften.
Turn the stovetop flame down to medium-low. Pour the egg mixture into the skillet covering the vegetables. Sprinkle in the goat cheese in pieces. Cook the eggs (not stirring) until almost set - about 4 minutes.
Broil the egg mixture 1-2 minutes or until the top begins to brown (a couple shades before the one in the picture!).
Remove the pan from the oven. Slice. Serve warm or at room temperature with a side salad.