Step 1: Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan or line it with parchment paper for easy removal.
Step 2: In a medium bowl, whisk together the flour, baking powder, baking soda, ground cardamom, and salt until well combined.
Step 3: In a large mixing bowl, beat the granulated sugar, brown sugar, and vegetable oil. Add the eggs one at a time, beating well after each addition until the mixture is smooth and light.
Step 4: Gradually stir the dry ingredients into the wet ingredients. Fold in the grated carrots until evenly distributed throughout the batter.
Step 5: Pour the batter into the prepared pan and bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Step 6: While the cake bakes, prepare the sauce by combining the chopped dates, water, and grated ginger in a small saucepan. Simmer over medium heat for 10-15 minutes until the dates are very soft and the liquid has reduced into a thick syrup. Stir in the lemon juice.
Step 7: Once the cake is slightly cooled, pour the warm ginger date sauce over the top, allowing it to soak in before serving.