Preheat the gallette iron over medium-high heat for 10 to 15 minutes.
In a large bowl, cream together the butter and sugar. Stir in the flour, then beat in the eggs, one at a time. Finally, stir in the vanilla.
Drop batter by rounded teaspoons onto the heated iron, two at a time. Close the iron, and hold on the burner for 30 to 45 seconds, turn over and cook for an additional 30 to 45 seconds. Carefully remove cookies and cool on wire racks.