Preheat the oven to 375 degrees F.
Line a baking sheet with parchment paper.
Unroll the crescent triangles and place them onto the prepared baking sheet.
In a medium bowl, add the butter, the brown sugar, and the cinnamon and mix to combine.
Use a spoon to spread the cinnamon mixture over the top of the crescent rolls.
Roll up the crescent rolls and place them seam-side down on the prepared baking sheet.
Bake the roll-ups until they are lightly golden around the edges, about 9-12 minutes.
Allow the roll-ups to cool slightly.
In a small bowl, add the powdered sugar, the milk, and the vanilla and whisk to combine.
Drizzle the glaze over the roll-ups.
Serve warm.