Heat oil in deep-fryer to 190oC.
In a large bowl, sift together flour, sugar, salt, baking powder, cinnamon and nutmeg. Mix in butter until crumbly. Stir in milk and egg until smooth. Knead lightly, then turn out onto a lightly floured surface. Roll or pat to 1 cm thickness. Cut with a doughnut cutter, or use two round biscuit cutters of different sizes.
Carefully drop doughnuts into hot oil, a few at a time. Do not overcrowd pan. Fry, turning once, for 3 minutes or until golden. Drain on paper towels
Whilst warm, coat in combined caster sugar and cinnamon.