For the rolls: Preheat the oven to 350 degrees F. Grease an 8-inch square cake pan with cooking spray or butter.
Mix the granulated sugar, melted butter, vanilla extract and peppermint extract in a bowl. Unroll the crescent dough sheets and coat each sheet in half of the butter mixture, spreading it to the edges of the sheets. Roll each sheet tightly, starting with the longer side, and place the seam side down. Cut each roll into 8 equal pieces, making a total of 16 pieces. Arrange the pieces in the prepared cake pan.
Bake until golden and cooked through, 22 to 24 minutes. Let cool completely, about 30 minutes.
For the glaze: Meanwhile, make the glaze by whisking together the powdered sugar, milk and peppermint extract, Add the melted butter and red food coloring, whisking until completely combined.
Remove the cooled rolls from the pan and top each one with the glaze. Sprinkle over the crushed candy canes and serve.