Sieve the flour into a bowl; stir in the sugar. Separate one egg and put the yolk in a jug (save the egg white for another recipe). Add the other whole egg and milk to the jug and whisk. Make a well in the flour and whisk in the milk and egg mixture to form a smooth batter. Stir in the butter and vanilla. Set aside to rest for 10 minutes.
Smear the oil in a 20cm non-stick frying pan and put over a medium heat until hot. Pour in enough batter to cover the base. Cook for 1 minute; flip and cook the other side for 30 seconds until cooked through.
Transfer to a warm plate and repeat until you have 8-10 pancakes. Serve with caster sugar and a drizzle of lemon juice.