In an ovenproof, heavy bottomed, 9-inch pan (23cm), such as a cast iron pan, heat 3 tablespoons of fat over medium-low heat.
Add onion and vegetable and sauté until tender, stirring occasionally; put the lid on the pan if needed to keep the vegetables from drying out.
Once the vegetables are tender, add the strongly-flavored aromatic herbs and 1 pinch of salt, and sauté for 1–2 minutes.
Meanwhile, in a bowl, mix eggs with cream or milk, 2 pinches of salt, and 1/8 teaspoon black pepper.
Stir sautéed vegetable mixture into egg mixture.
Heat the remaining 2 tablespoons of fat in the pan, add the egg-vegetable mixture, and cook over medium-low heat for about five minutes, until the bottom of the frittata is cooked.
Turn oven on to broil, sprinkle the cheese over the top of the frittata, and place in the oven about 4 inches away from the broiling flame. Broil the frittata until it puffs up and browns, about 5–7 minutes.
Serve straight from the oven. Cold leftovers are delicious too.
