Stir brown sugar and butter together in a large bowl until smooth and creamy. Add eggs and vanilla; beat well. Gradually stir in flour. Set bowl over a hot water bath; stir to combine. Cover and refrigerate overnight.

Preheat the galette iron according to manufacturer's instructions.

Roll dough into 1-inch balls; place in galette iron. Close the iron; cook cookies, about 30 seconds in an electric galette iron, or 2 to 4 minutes in a handheld iron over medium heat. Carefully remove cookies and cool on wire racks.