Using a vegetable steamer, steam the zucchini, carrots, and diced turnips until the vegetables are al dente.
Mix 2 or 3 tablespoons of water with the eggs in a bowl (amount of water depends on the size of the eggs), lightly beat together with a pinch of salt and a dash of pepper, then gently add the vegetables.
Grease a non-stick pan with oil; when the pan is hot, pour the mixture in and cook on a very low heat until the edges of the omelet show that the underneath is cooked. Flip it using a plate and cook the other side as well. This can be served hot or warm.