To make the cake, heat the oven to 175C/155C fan/gas 4. Lightly butter or oil a 23cm x 33cm cake tin and line the bottom with parchment paper.
Whisk together the eggs, sugar, oil, milk, salt, and vanilla until smooth. Add the flour, baking powder, cinnamon, nutmeg, allspice, and cloves and whisk together until smooth, about two minutes. Fold the parsnips and ginger into the batter.
Pour the batter into the tin – the batter won’t rise much, so you can fill the tin to within 1.3cm of the top. Bake until a toothpick stuck in the middle comes out with just crumbs clinging, about 24 minutes, rotating the pan halfway through baking.
Let cool in the pan for 10 minutes, then turn out