Beat eggs with cream in a bowl, add salt and pepper to taste and set aside.
In a large non-stick pan, melt half the butter and sauté vegetables for 2 to 3 minutes. Add sausages, cook for 1 minute and set aside, keeping warm.
Melt the rest of the butter with olive oil in the pan, pour in egg mixture and cook over low heat without stirring.
When omelette is nearly set, place vegetable mixture and sausages in the middle of the pan, then sprinkle with grated cheese.
Fold omelette in half and continue cooking for 1 to 4 minutes, depending how you like your omelette (1 minute for runny to 4 minutes for well cooked). Divide into four portions.
Serve omelette immediately, with fried potatoes.
Tips from the chef
To make individual omelettes, simply divide egg mixture and toppings in four and proceed as above.