Preheat the oven to 190C or 375F and line a 10x15 inch jelly roll pan (25x38 cm) with parchment paper, so the sides stick up enough for you to lift the cake after baking. If you don’t have a jelly roll pan (like me), you can make a box of the same size from parchment paper and place it on a baking sheet. It will be enough to stop the batter from running away during baking.
In a bowl, combine the flour, ground cinnamon, ginger, nutmeg, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer (or use a bowl and a hand mixer, or do it by hand with a whisk), add the sugar, honey, and eggs. Whip for 2 minutes or until foamy and the sugar has partially melted. Add the purée and whip again until well combined.
Add the dry ingredients to the wet ones and mix with a rubber spatula until no dry ingredients are left.
Pour the batter into the prepared jelly roll pan and spread it in an even layer across the surface.
Bake for 13-15 minutes or until no wet spots are visible on the surface and it’s springy to the touch.
Meanwhile, place a kitchen towel on your working surface and sprinkle it with powdered sugar. The size of the towel should be enough to roll the cake into it.
Remove the cake from the oven and check if the sides are stacked on the parchment paper. If yes, carefully unstack them without breaking the cake. Help with a small knife if needed.
Then lift the cake from the pan, holding onto the sticking parts of paper, and flip it onto the towel dusted with powdered sugar. Carefully peel off the parchment paper.
Roll the cake together with the towel and let it cool down like that on a cooling rack.