Warm the milk with the butter and sugar until everything is dissolved.
Mix the instant yeast with the bread flour. Add the warm milk mixture, vanilla, and salt, stirring until a slightly sticky dough forms.
Transfer the dough to a floured bowl, cover, and let rise in a warm place until doubled in volume.
Punch down the dough to remove the air, then knead briefly until smooth and elastic. Roll it out with a rolling pin into a 10ch in by 14 inch rectangle.
Brush the dough with 1 Tbsp + 1 tsp (25 gr.) melted butter and sprinkle lightly with sugar.
Roll both long sides toward the center, cut into 1¼-inch thick portions with a sharp knife, and place them on a tray lined with baking paper, spacing them apart to allow for expansion. Brush with beaten egg and let rest for 15 minutes while the oven preheats to 350°F.
After 15 minutes, brush again with egg and bake at 350°F for 18 minutes.
Melt the butter and milk together in the microwave or in a small saucepan.
Whisk in the cocoa powder until smooth.
Add the powdered sugar, vanilla, and salt.
Whisk until glossy and lump-free.
Ideal temperature: 35–40°C / 95–105°F
Dip the cooled palmiers once and let the excess drip off.
The icing sets in about 10 minutes at room temperature.