For the Dough:
In the bowl of a stand mixer fitted with a kneading attachment, combine flour, yeast, butter, sugar, milk, eggs, vanilla extract, and salt. Knead on low speed for 12-15 minutes until the dough is soft, smooth, and elastic.
Shape the dough into a ball, place it in a bowl, and cover with a towel. Let it rise for 1-2 hours, or until the dough has doubled in size.
Once risen, transfer the dough to a work surface and divide it into two parts. Roll each part into a thick log and cut each log into 6 pieces, making 12 rolls in total.
Shape each piece into a ball and place them on a baking tray lined with parchment paper. Cover and let rise for another 30 minutes, or until the rolls double in size.
For the Syrup:
In a small saucepan, combine water and sugar. Bring to a boil and let it cook for 1-2 minutes for a slight reduction.
Remove from heat and cool the syrup to room temperature.
Baking the Rolls:
Preheat the oven to 170°C (340°F).
Brush the risen rolls with the beaten egg and bake for 12-16 minutes, or until golden and set.
While the rolls are still hot, brush them generously with the cooled syrup. Allow them to cool completely to room temperature.
For the Vanilla Cream:
In the bowl of a stand mixer fitted with a whisk attachment, add the cold whipping cream, powdered sugar, vanilla pudding powder, and vanilla extract. Whip on high speed until the cream is thick, smooth, and stable.
Assembling the Maritozzo:
Once the rolls are completely cool, make a deep slit in the center of each roll, but leave the base intact.
Using a piping bag or a plastic baking card, fill the center of each roll with the vanilla cream. Smooth the exposed cream for a uniform look.
Dust the filled rolls generously with powdered sugar and serve immediately.