Preheat the oven to 180°C/160°C fan/350°F/gas 4. Grease three 20cm/8in cake pans and line the bases with baking parchment.
Finely grate the parsnip or whiz in a food processor until fine, then set aside. Peel, core and finely dice the pears.
In a large bowl, cream the butter and sugar with an electric mixer until pale and fluffy.
Beat in the eggs, one at a time, beating well after each addition, then stir in the parsnip, pears and vanilla.
Sift in the flour, baking powder and salt, and stir gently to combine.
Divide the batter between the prepared pans and bake for 20 minutes, or until golden and the centre springs back when touched.
Leave to cool in the pans for 5 minutes, then turn out onto a wire rack to cool completely.