Preheat the oven to 350ºF. Grease a 2-quart casserole or 10-inch pie dish with butter or shortening and set aside.
Sauté the carrots:
Melt 3 tablespoons butter in a skillet over medium-low heat. Once melted, add the carrots and cook for 7 to 8 minutes until softened. Set aside.
Make the batter:
Combine the flour, brown sugar, baking soda, baking powder, cinnamon, ginger, and nutmeg in a large bowl.
Add the egg, whole milk, and 1 teaspoon vanilla extract to the dry ingredients. Beat with an electric mixer until smooth, but don’t overwork the mixture.
Finish the batter:
Fold the dates, hazelnuts, and cooked carrots into the batter.
Bake the carrot pudding:
Pour the batter into the prepared casserole or pie dish. Transfer to the oven for 35 to 40 minutes or until a toothpick inserted in the center comes out clean.
Make the whipped cream:
Combine heavy cream, 1 teaspoon vanilla extract, and ¼ cup powdered sugar in a bowl. Beat with an electric mixer at medium-high speed until stiff peaks form. Transfer to the refrigerator until needed.
Cool the carrot pudding:
Remove the carrot pudding from the oven and let it stand for 20 to 30 minutes.
To serve:
Slice the carrot pudding and serve warm with whipped cream. If desired, scatter roughly chopped hazelnuts on each slice. Enjoy!