Step 1: Preheat your oven to 350°F (175°C) and grease an 8x8 inch square baking dish.
Step 2: In a medium bowl, whisk together the flour, baking powder, cinnamon, and nutmeg.
Step 3: In a large mixing bowl, cream the softened butter and 0.75 cup brown sugar until the mixture is light and fluffy.
Step 4: Add the eggs one at a time, beating well after each addition to ensure a smooth batter.
Step 5: Gently fold in the finely grated carrots and chopped dates until they are evenly distributed.
Step 6: Gradually add the dry flour mixture to the wet ingredients, stirring just until combined.
Step 7: Spread the batter into the prepared baking dish and bake for 40-45 minutes, or until a toothpick comes out clean.
Step 8: While the pudding bakes, combine 0.5 cup butter, 1 cup dark brown sugar, and 0.5 cup heavy cream in a small saucepan over medium heat.
Step 9: Bring the sauce to a gentle simmer and cook for 5 minutes until thickened and glossy.
Step 10: Once the pudding is out of the oven, prick the surface with a fork and pour the warm brown sugar sauce over the top before serving.