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

Melt the unsalted butter in a small saucepan over medium heat, then let it cool for about 15 minutes.

Finely grate the carrots and press them in a cloth to remove excess juice.

In a large bowl, whisk together melted butter, sugar, and eggs. Then mix in oil, carrot purée, grated carrots, and vanilla extract.

In a separate bowl, whisk together flour, baking soda, baking powder, cinnamon, and salt.

Gently fold the dry ingredients into the wet mixture until just combined.

Scoop the cookie dough onto the prepared baking sheet, spacing them about 2 inches apart.

Bake for 8-10 minutes until lightly golden and springing back when touched.

Let the cookies cool on the baking sheet for about 5 minutes, then transfer to a cooling rack.

Beat together cream cheese and butter until creamy. Gradually add powdered sugar, then vanilla extract and a pinch of salt.

Once completely cool, generously frost the tops of the cookies and add decorations if desired.