Bunny carrot cake

Name: Bunny carrot cake
Ingredients: 200g light soft brown sugar, plus 3 tbsp; 150ml light rapeseed oil (we used Cooks & Co with natural butter flavour), plus extra for greasing; 100g natural yogurt, plus extra to serve (optional); 3 large eggs; 2 tsp vanilla extract; zest 3 oranges, juice of 2 (save juice of last orange for the carrots, below); 300g self-raising flour; 1 tbsp mixed spice; 1 tsp ground cinnamon; 250g coarsely grated carrot; crème fraîche, to serve (optional); 225-250g small or baby carrots, peeled and halved lengthways; juice 1 orange (from cake ingredients); 25g butter; 4 tbsp light soft brown sugar