Put olive oil in a skillet and turn heat to medium. When fat is hot, add onion and cook. Sprinkle with salt and pepper and cook 3 to 5 minutes.
Add vegetables, raise heat and cook, stirring occasionally until they soften, from a couple minutes for greens to 15 minutes for sliced potatoes. Adjust heat so vegetables brown a little without scorching. If vegetables are precooked just add to onions and stir before proceeding.
When vegetables are nearly done, turn heat to low and add herb. Cook, stirring occasionally, until vegetables are tender.
Meanwhile, beat eggs with some salt and pepper, along with cheese if using.
Pour over vegetables distributing them evenly. Cook, undisturbed, until eggs are barely set, 10 minutes or so.
Run pan under broiler for a minute or 2 if top does not set. Cut frittata into wedges and serve hot, warm, or at room temperature.