Preheat the oven to 200C/400F/Gas 6. Grease a 12-hole muffin pan well, and set aside.
Whisk together the flour, baking powder, salt, and spices. Set aside.
In a large bowl, whisk together the eggs and sugar until thick and light in colour. Add the buttermilk, oil, and vanilla, and whisk until combined.
Add the dry ingredients in thirds and fold in until just combined - do not overmix. Fold in the grated carrots. The mixture will be thick and somewhat lumpy.
For the Crumb Topping
In a small bowl, whisk together the flour, sugar, and cinnamon. Add the melted butter, and mix until evenly distributed and the mixture is crumbly.
Spoon the muffin batter into the prepared pan (fill to the top for very tall muffins), top with the crumb mixture, and bake for 15 - 20 minutes, or until a toothpick inserted into the centre comes out clean.
Allow to cool for 5 - 10 minutes in the pan before transferring them to a wire rack to cool completely.
For the Cream Cheese Glaze
Whisk together the cream cheese and icing sugar until smooth and combined. Add the vanilla and milk, and mix until combined. Add more icing sugar for a thicker glaze.
Drizzle the glaze over the cooled muffins.
Video
Notes
*To make your own buttermilk, simply add 1 tablespoon of fresh lemon juice or white vinegar to 1 cup (240ml) of milk. Stir to combine, and allow to sit for 5 - 10 minutes until slightly thickened and curdled.Muffins stay fresh in an airtight container at room temperature for up to 5 days. They also freeze well for up to 2 months. Thaw overnight in the fridge.