Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
Unroll croissant dough onto a lightly floured surface.
In a small bowl, combine softened butter, brown sugar, and cinnamon.
Spread cinnamon-sugar mixture evenly over the croissant dough.
Starting from a short end, tightly roll up the dough and pinch the seam to seal.
Slice the roll into 4 equal pieces.
Place cinnamon roll slices onto the prepared baking sheet, leaving space between each.
Bake for 12-15 minutes, or until golden brown and filling is bubbly.
In a small bowl, whisk powdered sugar, milk, and vanilla extract until smooth to make the glaze.
Let cinnamon roll croissants cool slightly before glazing.