Preheat oven to 200 C / Gas 6. Line a muffin tin with paper muffin cases.
Beat egg in medium-sized bowl, then add milk, oil, pumpkin and vanilla. Stir thoroughly until mixture is smooth.
In a separate large bowl, mix together all remaining dry ingredients. Add all of the wet mixture to the large bowl of dry ingredients. Fold together gently until the flour mixture is just moistened, ensuring you do not over-mix (over-mixing will cause the muffins to not rise properly). The batter will be lumpy, not smooth.
Spoon batter into prepared muffin cases, filling nearly to the top.
Bake for 20 minutes, or until a skewer comes out clean at the centre of a muffin.