Oil an 18 cm (7 inch) square cake tin and line with greaseproof paper. Oil the paper.
Whisk together the oil and muscovado sugar to combine, then whisk in the eggs. Sift the flour and mixed spice into the bowl and stir in. Add the carrots and sultanas, and mix well. Pour the mixture into the tin and level the top. Place on the lower rack of the halogen oven.
Set the temperature to 175°C (347°F) and cook for about 30 minutes until just firm to the touch. Leave in the tin for 10 minutes, then transfer to a wire rack to cool.
Beat together the cream cheese, vanilla and icing sugar to make the frosting. Spread over the cooled cake with a palette knife. Serve cut into squares.