Beat the butter and sugar until fluffy and creamy. Add the milk and puréed tofu and mix. Add the vanilla, brandy, and lemon zest; mix well and set aside.
In a separate bowl, whisk together the flour, cornstarch, salt, baking soda, and baking powder. Add the dry mixture to the butter mixture and work together with your hands until combined and soft. Do not add any extra flour. Cover and chill in the refrigerator for 2 hours.
Preheat the oven to 325°F (170°C, or gas mark 3). Line baking sheets with parchment paper. Divide the dough in half and keep half refrigerated. On a floured work surface and using a floured rolling pin, roll out the dough to a thickness of 1/4 inch (6 mm). Cut into 2-inch (5 cm) rounds with a cookie cutter and transfer to the prepared baking sheets. Repeat with the remaining half of the cookie dough.
Bake for 12 to 15 minutes, or until golden. The cookies should be dry but not brown.