In a wide, non-stick pan, put olive oil to cover the bottom and sauté the sausages. Put them on kitchen towel to absorb the excess fat and oil.
Add some axtra oil in the pan, add the potatoes, salted and fry them until tender. Carefully tilt the pan and remove most of the oil.
In a bowl, beat the eggs very well with the milk, the mint, salt and pepper.
Put the sausages back into the pan by placing them between the potatoes. Pour the mixture of eggs, close the pan with a large lid (diameter larger than that of the pan) and bake the omelette on medium heat.
Check it if it is cooked with a spatula.
Turn the frypot upside down so that the omelette drops to the lid and then put it back in the pan to cook on the other side.
Put it on a platter and serve with bread and seasonal salad.