Preheat the oven to 375°F (190°C).
Line a baking sheet with parchment paper.
On a lightly floured surface, unfold the thawed puff pastry sheet.
Brush the melted butter evenly over the pastry sheet.
In a small bowl, mix together brown sugar and ground cinnamon.
Sprinkle the cinnamon-sugar mixture evenly over the buttered pastry sheet.
Roll up the pastry sheet tightly from one end to the other.
Slice the rolled pastry into 1-inch wide pieces, yielding mini rolls.
Place the mini cinnamon rolls on the prepared baking sheet, cut side up.
Bake in the preheated oven for 12 - 15 minutes, or until golden brown and puffed.
While the rolls are baking, prepare the dip.
In a small bowl, whisk together softened cream cheese and powdered sugar until smooth.
Add milk and vanilla extract, and whisk until well combined and smooth.
Once the cinnamon rolls are baked and slightly cooled, serve them warm with the prepared dip.
Pour cold milk into glasses to accompany the cinnamon rolls and enjoy.