Brioche Dough

1. Rehydrate the baker's yeast in lukewarm milk and let it rest for 5-10 minutes.
2. In the bowl of your stand mixer fitted with a dough hook, place the flour, sugar, and salt, and mix at medium speed.
3. Add the milk and yeast mixture, egg, and melted butter and knead for 5 to 7 minutes until you have a smooth dough that pulls away from the sides of the bowl but is a bit sticky.
4. Cover the bowl with plastic wrap or a kitchen towel and let the dough rise for 1.5 to 2 hours in a warm place (or in your oven heated to 104°F).

Filling

1. In a medium bowl, place all the ingredients: softened butter, brown sugar, ground cinnamon, and vanilla.
2. Mix with a spoon until you get a homogeneous and creamy mixture.

Assembly and Baking

1. Transfer the brioche dough to a lightly floured work surface and deflate the dough with your hands.
2. Roll out the dough with a rolling pin to form a large rectangle about 5mm thick.
3. Spread the cinnamon filling over the entire surface of the dough.
4. Then roll the dough tightly into a long log lengthwise.
5. Cut the log into 12 pieces, each 2-3 cm wide, using a large knife or dental floss.
6. Place each piece of brioche in a pre-greased cupcake/muffin tin.
7. Cover with a kitchen towel and let the rolled buns rise again for 30-45 minutes.
8. Preheat the oven to 356°F and bake the rolled buns in the middle rack for 20-25 minutes until they are well risen and golden on top.

Cream Cheese Icing

1. In a container, place the softened butter, cream cheese, powdered sugar, and vanilla.
2. Beat with a hand whisk or an electric mixer until you get a creamy and smooth icing.
3. Brush the top of the cinnamon roll muffins with the cream cheese icing and enjoy.