Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

Melt the unsalted butter in a small saucepan. Allow to cool for about 15 minutes.

Finely shred the fresh carrots and drain excess moisture using paper towels.

In a large mixing bowl, whisk together cooled melted butter, granulated sugar, eggs, canola oil, carrot purée, finely shredded carrots, and vanilla extract.

In a separate bowl, whisk together all-purpose flour, baking soda, baking powder, ground cinnamon, and salt. Fold into the wet ingredients.

Scoop dough onto the prepared baking sheet leaving space between each cookie.

Bake for 8-10 minutes, until the edges are set but the centers remain soft.

Transfer baked cookies to a wire rack to cool completely.

Beat cream cheese until smooth. Gradually mix in softened butter, vanilla extract, and powdered sugar.

Frost cooled cookies generously with cream cheese frosting and sprinkle with nuts if desired.