Heat milk and butter together in a microwave-safe container until lukewarm, about 110–115°F.

Pour the warm milk and butter into a stand mixer bowl, add the yeast, and whisk gently to combine.

Mix in the eggs and vanilla until fully incorporated.

Gradually add the flour, sugar, and salt, mixing with a dough hook until a smooth dough forms.

Cover the dough with plastic wrap and let it rise for about 1 hour, or until it has doubled in size.

Roll the dough into a 12 x 18 inch rectangle about ¼ inch thick on a lightly floured surface.

Mix brown sugar, room-temperature butter, and cinnamon until creamy for the filling.

Spread the filling evenly over the rolled-out dough using an icing spatula.

Starting from the long side, carefully roll the dough into a tight log.

Cut the log into 1–1.5 inch slices using a serrated knife and place on a greased or parchment-lined baking sheet.

Bake at 350°F (175°C) for about 30 minutes, until golden brown.

While baking, mix together the icing ingredients until smooth.

Let the rolls cool for a few minutes, then drizzle or spread the icing on top.