Warm the whole milk until lukewarm, about 35–40°C (95–104°F).

Dissolve the active dry baker's yeast in the 200 ml whole milk.

Rest the yeast mixture for 10 minutes, until slightly foamy.

Combine the all-purpose flour, 45 g granulated sugar, vanilla sugar, and salt in the large mixing bowl.

Add the 2 eggs to the dry ingredients and mix until combined.

Pour in the activated yeast mixture and mix into a shaggy dough.

Knead the dough for 5 minutes until homogeneous.

Add the softened unsalted butter in small pieces to the dough.

Knead for 5 more minutes until the dough is soft and slightly elastic.

Cover the dough with the clean kitchen towel.

Let the covered dough rise at room temperature for 60–90 minutes, until doubled in volume.

Turn the risen dough onto a lightly floured surface and divide it into 12 equal portions.

Shape each portion into a round doughnut or beignet shape.

Heat the neutral frying oil in a deep pan to 175°C (350°F).

Fry the shaped beignets in small batches until golden underneath.

Turn the beignets and fry until both sides are deeply golden, about 2–3 minutes total per batch.

Lift the fried beignets out with the slotted spoon and drain them on paper towels.

Coat the warm beignets generously with the 100 g granulated sugar for coating.