I made a huge batch with the kids on Saturday morning - went down a storm! I got around 16 round ones out of this mix (big ones!) and the last two got eaten today lol
Here's the recipe I used :
2 (7g) sachets dried active baking yeast
4 tablespoons warm water (45 C)
350ml (12 fl oz) lukewarm milk
100g (4 oz) caster sugar
1 teaspoon salt
2 eggs
75g (3 oz) butter
575g (1 1/3 lb) plain flour
1L (1 3/4 pints) vegetable oil for frying
1 1/2 teaspoons vanilla extract
Sprinkle the yeast over the warm water, and let stand for 5 minutes, or until foamy.
In a large bowl, mix together the yeast mixture, milk, sugar, salt, eggs, butter and 1/2 of the flour. Mix for a few minutes at low speed, or stirring with a wooden spoon. Beat in remaining flour a little at a time, until the dough no longer sticks to the bowl. Knead for about 5 minutes, or until smooth and elastic. Place the dough into a greased bowl, and cover. Set in a warm place to rise until double. Dough is ready if you touch it, and the indention remains.
Turn the dough out onto a floured surface, and gently roll out to 1cm (1/2 in) thickness. Cut with a floured round cutter. Let doughnuts sit out to rise again until double. Cover loosely with a cloth.
Heat oil in a deep-fryer or large heavy pan to 175 C. Slide doughnuts into the hot oil using a wide spatula. Turn doughnuts over as they rise to the surface. Fry doughnuts on each side until golden brown. Remove from hot oil and drain on a wire rack. I popped them straight out onto kitchen roll and then threw them into a tray of caster sugar with a teaspoon of cinnamon mixed in for half of them (filled them with sweet cooked apple) and the rest went into plain caster sugar and filled with Wilkin & Sons raspberry seedless jam

(there's none better for doughnuts ;D)
BTW - I found I had to use a fair bit more flour than stated in the recipe too