Just before bedtime, preheat the oven to 200 degrees. Grease a 9 inch springform pan. Dust with the cracker crumbs. Set it aside.
In a large bowl, combine the cream cheese and sugar until smooth. Stir in the vanilla extract, brandy, and eggs until well-blended. Pour the batter into the prepared pan and place in the oven overnight.
The next morning, 6 to 8 hours later, the cake will be set and the top will have just colored. Remove to a rack and cool in the pan until the pan is cool enough to handle, 1 hour.
Cover with plastic wrap or waxed paper and an inverted plate. Invert. Remove the pan and refrigerate, upside down, for at least 1 hour.
Invert a serving plate over the cheesecake and invert the whole thing. Remove the top plate and the paper. Cover and refrigerate until ready to serve.