Preheat the oven to 350°F (175°C) and line a half sheet pan with parchment paper.

Melt the unsalted butter over low heat and let it cool for about 15 minutes.

Shred the carrots finely and press out excess moisture using paper towels.

In a large mixing bowl, combine the melted butter, granulated sugar, eggs, canola oil, carrot purée, grated carrots, and vanilla extract. Whisk until smooth.

In a separate bowl, whisk together flour, baking soda, baking powder, cinnamon, and salt. Fold this dry mixture into the wet ingredients.

Using a cookie scoop, portion out the dough onto the prepared pan, leaving spaces in between.

Bake for approximately 8–10 minutes until lightly firm but soft in the center.

Let the cookies cool on the pan for about 5 minutes before transferring to a wire rack.

For frosting, blend cream cheese and unsalted butter until smooth, then add powdered sugar and vanilla until fluffy.

Frost the cooled cookies generously and top with walnuts or pecans if desired.