Preheat the oven to 375°F. Place a large oven-safe skillet or sauté pan over medium heat. When the pan is hot, add the oil and onion; cook until translucent, about 3 minutes. Add the andouille and mushrooms and continue sautéing, about 5 minutes. Season with salt and pepper. Beat the eggs vigorously with a fork or whisk, then add to the skillet, along with the goat cheese and chives, if using. Place in the oven and bake until the eggs have fully set (a toothpick inserted into the middle will come out clean), about 20 minutes. Let cool and then slice into 4 portions, topping with more chives if you like.