Heat the oven to 180C/350F/Gas 4. Line two mini-muffin tins with squares of baking parchment, pushing them down to make little cases (alternatively use shop-bought mini-muffin cases).
Mix the flours, baking powder, mixed spice and salt together in a bowl.
Whisk together the egg and butter in a separate bowl. Stir in the parsnips, apple, raisins and honey and then add to the dry ingredients. Add the apple juice and stir to combine, but take care not to overmix.
Spoon the mixture into the muffin tins and bake for 18-20 minutes, or until risen (check after 15 minutes).
For the topping, beat the butter in a bowl until smooth and creamy.
In another bowl, beat the cream cheese until creamy then stir in the honey and vanilla extract. Add the creamed butter and stir to combine. Transfer the topping into a piping bag fitted with a large star tip. Refrigerate the piping bag for about 30 minutes (leaving the piping bag in the fridge makes the topping easier to pipe).
Pipe the topping onto the muffins.