For the cake:
Preheat oven to 180C/350F. Grease and line a 9" square cake tin with parchment paper.
Beat the eggs, sugar, yogurt, oil and vanilla together well. Stir in the grated swede. Sift in the flour, baking powder, bicarb of soda, nutmeg and salt and gently stir to combine.
Pour into the prepared tin and bake for 25-30 minutes or until an inserted skewer comes out clean. Cool for 10 minutes in the tin and then turn onto a wire rack, removing the parchment paper, to cool completely.
For the frosting
Put the icing sugar, vanilla and 1 tablespoon of the milk into a large bowl. Set aside.
In a saucepan over a low heat, melt the butter and continue to heat until it turns brown and smells nutty. Pour into the bowl of powdered sugar and beat until thick and smooth, adding more milk if necessary.
Top the cooled cake with the frosting and sprinkle with the chopped hazelnuts.