Preheat your oven to 375°F. Line a baking sheet with parchment paper.
Pop open the crescent roll tube and carefully unroll the dough. Separate into 8 individual triangles and lay them flat on the prepared baking sheet.
In a small mixing bowl, combine softened butter, light brown sugar, and ground cinnamon. Mash together with a fork until well combined and no butter chunks remain.
Using a spoon or butter knife, spread the cinnamon filling across each triangle, starting from the wide end. Leave about 1/4-inch border around the edges. Use a thin, even layer.
Roll each triangle starting from the wide end, rolling gently but firmly. Place each rolled crescent seam-side down on the baking sheet.
Bake for 9-12 minutes until lightly golden-brown. Check at 9 minutes and continue baking if needed.
While rolls bake, whisk together powdered sugar, 1 tablespoon milk, and vanilla extract in a small bowl. Add more milk gradually if too thick. Glaze should be pourable but not watery.
Remove rolls from oven and let cool for 3 minutes. Drizzle glaze over each roll in a zigzag pattern. Serve warm.