Boil the potatoes in their skins, freshly cooked (they are ready if you are able to insert the fork into the potatos without finding too much resistance) pull them out of the water and let them cool and then remove the peel.
Mash the potatoes, add the butter, salt, pepper, nutmeg and egg yolks and knead everything.

Place the dough in pastry bag with star tip and make tufts of about 5 cm in diameter by placing them in a pan lined with parchment paper.
Bake for about 20 minutes in a preheated oven at 200° C, preferably with the fan grill on, until they are golden tufts.
Serve your potatoes still warm.

SOME TIPS
It is important not to boil the potatoes for too long because they could soak up the water and this would result in a very soft dough. Moreover, it is not recommended to use new potatoes (because of the higher water content).

A precaution may be to boil the potatoes the day before, so they can have a little time for losing some of the water. Some advise to bake the potatoes boiled for some time to let them dry, and once mashed to cook them for a few minutes in a saucepan.

However, if cooking in the water shall not extend beyond what is necessary, these steps of further cooking is not required, but you can evaluate whether to consider them according to the consistency of mashed potatoes.

The quality of the potato affects the result, I prefer to use for this recipe potatoes with red skin and with yellow flesh because they give a great substance to the mix, it will result very hard and will keep the typical shape of a flame of potato duchess even after the cooking in the oven. Moreover with this type of potato the Duchess have a good crunchiness outside and remain soft inside.

Duchess potatoes made with white potatoes may sag after baking, especially if the potatoes have retained a lot of water during the boiling.
A very important aspect is the step in the oven, the potatoes Duchess should not cook, they should just acquire color. Therefore you can use (and it is preferable) the fan grill (the grill helps browning, ventilation helps dry the surface), and if you can not use the grill, make sure the oven is hot when you put the potatoes.

Nice to look at and good to eat, the duchess potatoes are neither boiled potatoes or baked potatoes, but simply both, a crispy surface with a soft heart.
They are a very popular side dish in French cuisine and are a great accompaniment for meat and fish. Duchess potatoes because of their particular shape flame are very scenic and often used as a garnish for dishes and buffet. The orgine of Duchess potatoes remains unknown, it seems to have been designed in honor of a lady, a Duchess in fact.

The potato (Solanum tuberosum) from the botanical point of view belongs to the Solanaceae family, is a herbaceous plant that produces many underground tubers which are the edible part of the plant.
The main nutrients of potatoes are carbohydrates that represent 84% of the dry weight of which 98% is starch and are therefore typically a food energetic although containing very little fat (only 1g per 100 g of product).
But potatoes are also a source of dietary fiber that helps counteract constipation, reduces the absorption of cholesterol and protects against the risk of colon cancer, in addition, provide a rich source of phosphorus and potassium, the latter needed by the body for combat hypertension, and especially the B group vitamins (vitamin B6, thiamin, niacin and folate) and vitamin C, to a lesser extent is the intake of vitamin A, however red potatoes (the ones used in this preparation) contain larger amounts of carotenoids which are important antioxidants and some of them are precursors of vitamin A.

Potatoes, belonging to the Solanaceae family, produce anti-nutritional substances such as toxic alkaloids solanine, and chaconine solanidine. These are mainly present in the leaves, stems and fruits and are poorly represented in the tubers whereas they begin to be formed only after an exposition to light.

It is good practice to store potatoes in the dark. Furthermore, the solanine accumulates more in the superficial zone, so you can remove a certain proportion eliminating a greater thickness of the peel.

The presence of solanine is easily detected by the appearance of the tuber, potatoes old, shriveled and wrinkled contain greater amounts of the alkaloid. Moreover, its amount is proportional to the number of buds on the tuber and the width of the green parts (determined by chlorophyll). These indicate that the potato has been exposed to sunlight and that has begun to synthesize the glycoalkaloids, so it is best to discard these parts, or if they are particularly large it is advisable to throw away the entire potato.

However, being a water-soluble alkaloid, solanine much of it ends up in the cooking water (in the case of potatoes) also these molecules are switched off by the heat, so there are no health risks in consuming the potatoes if they have levels of solanine in normality and if they are well cooked.