Lightly grease a donut pan and set it aside.
In a medium mixing bowl, stir together the flour, baking powder, cinnamon, ginger, salt and nutmeg until well combined.
2 cups (240 grams) flour, 1 teaspoon baking powder, 2 teaspoons cinnamon, 1 teaspoon ground ginger, 1 teaspoon salt, 1/2 teaspoon nutmeg
In a large mixing bowl, stir together the granulated sugar, brown sugar, oil, vanilla extract, milk, and eggs until the mixture is smooth and well blended. Stir in the grated carrots.
1/2 cup (100 grams) granulated sugar, 1/2 cup (100 grams) brown sugar, 1/3 cup (66 grams) oil, 1 teaspoon vanilla extract, 1/4 cup (57 grams) milk, 2 large, 1 1/2 cups (150 grams) finely grated carrots
Gradually add the dry ingredients to the wet ingredients, stirring until a thick batter forms. Fold in the chopped pecans.
Using a spoon or a small scoop, fill each cavity of the donut pan about 3/4 full (approximately 1/4 cup or 75 grams of batter per donut). Bake in the preheated oven for 13 to 15 minutes, or until the donuts spring back when gently pressed with a finger. Carefully remove the donuts from the pan and transfer them to a cooling rack. They can be stored in an airtight container at room temperature for up to 24 hours, or refrigerated for up to 3 days.