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

Melt your unsalted butter in a small saucepan over low heat and let it cool for about 15 minutes.

Finely grate your carrots and squeeze out excess moisture between paper towels.

In a mixing bowl, combine the cooled melted butter, sugar, eggs, oil, carrot puree, grated carrots, and vanilla extract; whisk until smooth.

Sift together the flour, baking soda, baking powder, cinnamon, and salt in another bowl.

Slowly mix the dry ingredients into the wet until just combined; don't overmix.

Scoop the dough onto the prepared baking sheet, spaced 2 inches apart.

Bake for 8-10 minutes until puffed and springy; let cool on the sheet for 5 minutes before transferring to a wire rack.

Beat together cream cheese and butter until smooth, then gradually add powdered sugar and vanilla; mix until fluffy.

Once cookies are completely cool, frost with cream cheese frosting and add nuts if desired.