Beat together eggs, cream or milk, and salt and pepper. Set aside.
In a non-stick 9- or 10-inch skillet, heat olive oil over medium heat. Sauté green onions until wilted, about 2 minutes. Stir in spinach leaves, nutmeg, (and mushrooms if used), and continue to sauté until spinach is wilted to your liking. Turn mixture out onto a serving dish.
In same skillet, over medium-low heat, add eggs and shake pan to cook omelet, stirring if necessary so uncooked egg runs underneath. When omelet is just beginning to set in the center, return spinach mixture to the pan and place on top of omelet. Sprinkle with the bacon if used, and the cheese. Cover pan and steam until cheese melts.
Slide omelet out onto serving dish and fold over in half or thirds. Top with additional cheese and bacon if desired.