Preheat the oven to 200C/180C Fan/Gas 6. Line a 6 hole muffin tin.
In a large bowl, combine the dry ingredients (flour, baking powder, sugar and a pinch of salt).
Make a well and add in the liquid ingredients (melted butter, milk, oil and egg).
Add the grated carrots. Stir together very gently with a wooden spoon, until only just combined.
Make the cream cheese filling by combining all ingredients in a bowl.
Create the muffins: add 1 tablespoon of muffin batter to each muffin liner. Add 1-2tsp of the cream cheese filling, then cover with remaining muffin batter. Optional: add a little of the remaining cream cheese filling to the top of the muffins and swirl with a knife/chopstick for pretty muffins!
Bake 15-20 mins, until golden! Let cool on a wire rack before serving (although fabulous whilst still slightly warm).