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 soda, baking powder, cinnamon, ginger, and salt until well combined.
Step 3: In a large mixing bowl, beat the eggs with the granulated and brown sugars until pale and fluffy. Gradually pour in the vegetable oil and vanilla extract while continuing to whisk.
Step 4: Gently fold the dry ingredients into the wet ingredients until just combined, being careful not to overmix the batter.
Step 5: Stir in the grated carrots, diced apples, and chopped dates until they are evenly distributed throughout the mixture.
Step 6: Pour the batter into the prepared pan and bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean.
Step 7: While the cake cools, prepare the vanilla cream by beating the cream cheese and butter together until smooth. Gradually add powdered sugar and vanilla bean paste, whisking until light and airy.
Step 8: Once the cake has cooled completely, spread the vanilla cream generously over the top and serve.