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

Melt unsalted butter and let it cool for about 15 minutes.

Finely grate carrots and press them between paper towels to remove excess moisture.

Mix together melted butter, sugar, eggs, oil, carrot puree, grated carrots, and vanilla extract until combined.

In a separate bowl, whisk together flour, baking soda, baking powder, cinnamon, and salt. Then combine with wet ingredients.

Scoop portions of dough onto the baking sheet, spacing them at least 2 inches apart.

Bake for 8-10 minutes until lightly golden and firm to the touch. Cool for 5 minutes on the baking sheet.

Beat cream cheese until smooth, add softened butter, then vanilla extract and salt. Gradually add powdered sugar.

Frost the cooled cookies and optionally garnish with walnuts or pecans.

Serve fresh or store in an airtight container.