In a large bowl, beat together butter and brown sugar until light and fluffy.

Add grated carrots and vanilla extract, and mix until well combined.

In a separate bowl, whisk together flour, cinnamon, and salt.

Gradually add this mixture into the wet ingredients and mix until a soft dough forms.

Divide the dough in half and shape into a square.

Wrap in plastic wrap and refrigerate for at least 2 hours (or overnight for best results).

Preheat oven to 325°F (163°C).

Line a cookie sheet with parchment paper.

Slice or roll the dough into cookies and place on the prepared sheet.

Bake for 10-12 minutes or until the edges are light golden brown.

Transfer cookies to a wire rack and dust with powdered sugar.

Let them cool completely before serving.