Preheat the oven to 350℉ (177℃). Line baking sheet pans with silicone baking mats or parchment paper.
In a medium mixing bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, ground cinnamon, and nutmeg. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment or in a large mixing bowl with an electric mixer, cream the unsalted butter, light brown sugar, and granulated sugar until smooth and creamy. Add in the egg, vegetable oil, and vanilla extract and mix until combined and smooth. Stir in the finely grated carrots.
Add half of the flour mixture into the carrot mixture and mix on low speed until mostly combined. Pour in the milk and mix until mostly combined. Then, add the remaining flour mixture and mix until the ingredients are well combined. Scrape the sides and bottom of the bowl to ensure the ingredients are well incorporated.
Portion the cookie dough using a large cookie scoop (3 tablespoons) and place on the prepared baking sheet pans, allowing room for spreading. Bake the cookies for approximately 12 to 13 minutes until the cookies are puffed up. Cool the cookies on the pan for 2 minutes and then transfer to a wire rack to cool completely.