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

Melt ½ cup of unsalted butter in a microwave-safe bowl, then allow it to cool for about 15 minutes.

Grate enough carrots to yield approximately 40 grams (about 1 medium carrot), then squeeze out any excess moisture.

In a large mixing bowl, combine the cooled melted butter, 1 cup of granulated sugar, 1 large egg, ¼ cup of neutral oil, 1 jar of carrot purée, the grated carrots, and 1 teaspoon of vanilla extract. Whisk until smooth.

In a separate bowl, whisk together 1 ½ cups of all-purpose flour, 1 teaspoon of baking soda, ½ teaspoon of baking powder, 1 teaspoon of ground cinnamon, and a pinch of salt. Fold into the wet mixture until just combined.

Portion out the cookie dough onto the prepared sheet pan, spacing each scoop about 2 inches apart.

Place the pan in the preheated oven and bake for 8-10 minutes until edges are lightly golden. Let cool on the pan for 5 minutes before transferring to a wire rack.

Make frosting by beating 8 ounces of softened cream cheese until smooth, then add ¼ cup softened butter and mix until creamy. Gradually incorporate 2 cups of powdered sugar until your desired consistency.

If desired, color frosting with gel food coloring and pipe it on top of each cookie. Add any additional decorations if desired.