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

Melt the unsalted butter until fully liquid and cool it for about 15 minutes.

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

In a large mixing bowl, whisk together melted butter, sugar, eggs, canola oil, carrot purée, and vanilla extract until smooth.

In another bowl, stir together flour, baking soda, baking powder, cinnamon, and salt. Gradually add to the wet ingredients.

Scoop out 2-tablespoon portions of dough and place them on the prepared pan, spacing them 2 inches apart.

Bake for 8-10 minutes until lightly golden and springy to touch.

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

Blend cream cheese and softened butter until smooth, then mix in powdered sugar and vanilla extract to your desired consistency.

Once cookies are cool, spread a tablespoon of cream cheese frosting on each cookie.