Divide the phyllo pastry sheets into 2 parts. Put 1/2 the sheets in a suitable baking dish.
Heat the butter until when you drop a bread crumb on it it darkens. Pour the heated butter over the baklava. Bake in a moderate oven until golden.
To make the sugar syrup, add 3 cups water to the sugar. Add the vanilla. Once the syrup comes to a boil and begins to thicken, remove it from the heat. Pour the hot syrup over the cooled baklava.
Leave it for a few hours before serving, so it can take in the syrup.