Heat the oven to 200C/fan 180C/gas 6. Line a regular muffin tin with paper cases or strips of baking parchment.
Put the sugar, oil, melted butter, eggs and milk in a bowl and whisk until smooth. Add the orange zest, walnuts, dates and carrots and mix. Sift the flour, baking powder and cinnamon together, and lightly fold into the muffin mixture. Do not over-mix the batter as it should be slightly lumpy. Divide throughout the tin.
Bake for about 20-25 minutes until a skewer comes out clean. Cool in the tins then transfer to a cooling rack until completely cold. To make the frosting, beat together the cream cheese, honey and orange zest and spread on top of each muffin.