Preheat the oven to 200 degrees celcius, and line a standard muffin pan with paper liners.
Place the coconut oil in a large bowl and if it's solid, melt in the microwave for 30-40 seconds.
Whisk in the coconut sugar, then add the eggs and whisk vigorously until frothy. Add the milk and vanilla, and whisk until incorporated.
Pour the oat flour over the top of the wet ingredients, and sprinkle over the baking powder, spices, baking soda and salt. Stir gently until almost combined, being careful not to over mix, then fold in the carrot and coconut.
Divide the batter between the (12) muffin cavities and top with walnut pieces.
Bake for 15-20 minutes, or until golden brown and the top of the muffin springs back when pressed gently. Remove from heat and cool on a wire rack for 10 minutes, then remove from the pan and cool completely.