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1
For the cake: Preheat the oven to 350 degrees F. Grease (with some vegetable oil) and flour a 9-by-13-inch cake pan.
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2
In a medium saucepan, bring the parsnips and milk to a simmer over medium heat.
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3
Cook until tender, about 5 minutes.
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4
Remove from the heat, cover the pan and let stand until cool.
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5
Drain the cooled parsnips, discard the milk and transfer them to a blender.
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6
Add 2 of the eggs and blend until very smooth.
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7
Transfer to a large bowl.
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8
Add the carrots, granulated sugar, salt, star anise, ginger, almond extract, white pepper, 3/4 cup vegetable oil and the remaining 2 eggs to the blender and blend on high speed until very smooth.
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9
Pour the carrot mixture into the pureed parsnips and stir well until combined.
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10
Sift together the 2 cups flour and baking powder into a bowl.
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11
Add the dry ingredients to the wet and, using a large rubber spatula, fold together until well incorporated.
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12
Pour the batter into the prepared pan and bake, rotating the pan halfway through, until golden brown and a tester inserted into the center comes out clean, 45 to 50 minutes.
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13
Let cool completely on a cooling rack before removing the cake from the pan.
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14
For the icing: Cream the cream cheese and butter together well.
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15
Add the confectioners' sugar and salt and mix well, making sure there are very few lumps.
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16
Combine the carrot juice with the vanilla, bitter almond and anise extracts and mix in a little at a time.
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17
Stir in the grated carrot last.
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18
Put back in the fridge to firm up.
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19
Frost the cake with the icing.
