Place dried shiitake in a bowl with hot water and set aside.
Melt 2 tablespoons butter in a large nonstick frying pan over high heat. Sauté onion until soft and starting to colour, add chicken and sauté until browned.
Remove shiitake from water and squeeze out excess water. Chop finely and add to chicken. Mix through.
Add cauliflower rice and cook another 5 minutes until cooked and coloured through. Remove to a plate. Wipe frying pan clean.
Whisk eggs, cream salt and pepper in a bowl until beaten well. Melt 1 tablespoon butter in the frying pan and pour in ¼ of the egg, covering the bottom of the pan. Cook for about 1 minute then add ¼ of the chicken and cauliflower mixture down the right side of the omelette.
Cook until set on the bottom and very carefully lift and fold over the left side to seal the omelette. Slide off the frying pan onto a plate.
Repeat with remaining egg and chicken mixture to make 4 omelettes.