Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.

In another bowl, beat the eggs and sugar until light and fluffy. Gradually add the oil and grated carrots.

Fold the dry ingredients into the wet mixture until just combined.

Spread the batter evenly onto the prepared baking sheet.

Bake for 12-15 minutes or until a toothpick inserted in the center comes out clean.

Remove from the oven and immediately roll the cake with the parchment paper into a log. Let it cool completely.

In a mixing bowl, beat the softened cream cheese until smooth.

Add the powdered sugar and vanilla extract, mixing until well combined. Adjust consistency with milk if needed.

Once the cake is cool, unroll it carefully and spread the cream cheese filling evenly over the surface.

Roll the cake back up tightly, without the parchment paper, and wrap it in plastic wrap.

Refrigerate for at least 1 hour before slicing and serving.