Heat some oil in a small frying pan over medium-high heat. Add in the mushrooms. Sauté until the mushroom slices have released waters and are just starting to turn golden, about 5 minutes. Transfer to a plate.
In the same pan, heat a bit more oil and add in the asparagus. Sauté until the asparagus is just starting to brown, about 4 minutes. Transfer to a plate.
In a large bowl, beat together the eggs.
In a large 12-inch (30-cm) frying pan, heat about ½ tablespoon of oil on medium to medium-high heat. Once the pan is hot, pour on the egg mixture. It should spread across the entire bottom of the pan. Allow it to cook about 2-3 minutes, undisturbed. The eggs should be fully set on the bottom, and starting to look set on the top.
On half of the omelette, top the mushrooms, asparagus, tomatoes, chicken and cheese. Gently fold the omelette over, leaving about a 2-inch gap so you can see what is inside the omelette.
Turn the heat down to medium. Allow the omelette to cook for another 5 - 7 minutes, until the eggs look fully cooked through. You can cover the skillet to speed up the cooking process.
Remove from heat and top with salt and pepper, as desired. Serve immediately.