Start by soaking 2/3 of the cuttlefish roes for 3 hours in cold water. Change the water every hour. Dry the roes very well, cut into cubes and set aside.
 
Mix the egg yolks with the cream and set aside in the refrigerator.
 
Place a generous amount of olive oil in a high saucepan and bring to low heat. Add onion and sliced garlic, thyme and bay leaves. Sauté these ingredients well over very low heat for 15 to 20 minutes. With the help of a spoon try to break the onion. When the onion does not resist, the braise is ready.
 
Remove the bay leaves and the thyme.
 
Increase the heat to the maximum, add the cuttlefish roes in cubes and sauté for 4 to 5 minutes, always stirring with the help of a spatula. If the cuttlefish roes are overcooked, they will have a rubbery texture.
 
Remove from heat and add the yolk and cream mixture gradually and constantly stirring. The pan temperature must be sufficient to cook the eggs.
 
If the formula does not have a creamy texture, bring the pan to low heat until you get the same texture.
 
Add straw potatoes and fresh parsley, mix and serve immediately.
 
Finish the dish with grated cuttlefish roes and serve with a small halophyte salad.