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

Melt the unsalted butter in a microwave-safe bowl and let it cool for about 15 minutes.

Grate the carrots finely and press them in a paper towel to remove excess moisture.

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

Sift together the all-purpose flour, baking soda, baking powder, cinnamon, and salt in another bowl. Gradually add to the wet ingredients, folding gently.

Scoop out portions of the dough onto the prepared baking sheet, leaving space between each.

Bake for about 8-10 minutes until light golden, and cookies bounce back slightly when pressed.

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

Mix together softened cream cheese and butter in a bowl until smooth, then add powdered sugar and vanilla extract.

Spread the cream cheese frosting generously over cooled cookies, and add optional toppings.