You mean you would like to make Vegetable Baked Eggs? Or Shirred Eggs with Vegetables? Whatever you call it, it is absolutely possible. To call them omelets is what is not possible.

Eggs are so versatile, you can do almost anything with them. We would grate a little carrot, zucchini and/or summer squash (little ones that don't have much in the way of seeds), maybe some onion, or cut some asparagus, maybe slice a little mushroom, or red and/or green pepper, and sauté them briefly, until they are – to use the current buzzword – tender-crisp.

If you want to be creative, you can cook a half-dozen vegetables separately (one after the other – it doesn't have to be a big deal) and then take requests for from your customers for made-to-order baked eggs.

Butter the muffin pan thoroughly; you don't want to have trouble getting the eggs out. Another option is to make them in custard cups or ramekins on a baking sheet, and, as long as the girls can be careful, you can serve the eggs on little plates right in the cups. Place a nest of vegetables in the bottom, and add one or two eggs, depending on the size of the container. You are going to have to decide whether to keep the eggs whole or scramble them before adding them to the pan (tradition keeps them intact). You'll want a little salt and pepper. Many baked egg recipes call for you to add a bit of cream before you add the eggs or a bit of extra melted butter. The addition of grated cheddar or crumbled feta cheese would not be entirely unique, either, but that doesn't mean you have to shy away from it.

In a 350°F (175°C) oven, you would bake single eggs for about 5 to 10 minutes and double eggs for 10 to 15 minutes. The time will vary depending on how quickly the dish conducts the heat. You want to take them out just before they're done, as they will continue to cook in their own heat and that of the muffin pan outside the oven. Serve immediately.

It would be over the top and not very virtuous to line each of the muffin cups with a piece of lightly cooked bacon before adding the other ingredients.

After finally learning how to make omelets correctly, we have relatively little sympathy for some of the things people (and restaurants!) pass off as or try to call omelets. An egg baked in the oven is not an omelet – and never will be.

In case our musings are not structured enough for you, you can also try this recipe: Baked Eggs in Cocotte, paying particular attention to the Variation.