Here is another of my natural recipes. I had this one for dinner yesterday.
In a small omelet pan melt a generous amount of butter, say two pats. Wash a zucchini squash, thinly slice it and add the slices to the pan. Fry the squash over moderate heat, turning once so both sides cook. I cook until the slices are limp enough to indicate they've been cooked throughout. Usually a few have just a bit of browning. Remove the squash when done cooking and place them on your dinner serving plate.
In the hot squash flavored butter that remains in the omelet pan, pour two or three eggs (depending how hungry you are) that you had previously beaten in a bowl, just like making scrambled eggs. Let cook without stirring, just occasionally tipping the omelet pan so that the eggs stick partly up the side of the pan. After about 3 to 5 minutes you will see that the bottom half is pretty cooked and the top half is still raw. Using a spatula loosen the sides, then reach under with the spatula and flip the omelet in the pan. Sometimes I get a perfect omelet to flip easily, other times I get only a half flipped and the other separates, and sometimes I get scrambled eggs! But it is cool if you can get the omelet complete. It comes with experience and a little luck and a good pan. (I used Emeril cookware and love it). Once you flip the omelet the bottom half will cook extremely fast, usually in less than a minute so I usually flip it and then turn off the stove burner. Once it is cooked through place it next to the zucchini on the plate. Salt to taste.
Now, you can keep them separate and enjoy each on their own. That is fun because the eggs will have taken on a subtle zucchini flavoring that a top chef would be proud of and you can enjoy it as is. Or you can use the cooked squash as filling for the omelet, placing the squash on one half the omelet and then folding the omelet over in half.
As a variation you can use olive oil instead of butter. I'm a traditional cook who likes the buttery texture, cooking integrity, nutrition and subtle flavor, but I also use olive oil for just about everything else, including popping popcorn in it.
Another variation is the use of vegetable. I often cook onions this way. Sometimes I leave the chopped onions in the pan and pour the egg over it so the onion pieces are embedded in the omelet. Or you can cook and use to fill the omelet as described above.