How to Make It
Combine butter, brown sugar, and honey in a saucepan. Cook over medium, stirring occasionally, until butter is melted, about 3 minutes. Remove from heat, and let cool completely, about 15 minutes.
Stir together corn flour, baking powder, and salt in a medium bowl until well combined; set aside.
Combine eggs, sugar, and vanilla bean paste in the bowl of an electric stand mixer fitted with the whisk attachment. Beat on high speed until fluffy and pale, about 2 minutes. With mixer running on medium speed, add cooled butter mixture in a slow, steady stream. Stir in corn flour mixture until combined. Chill mixture until firm and cold, about 3 hours.
Preheat oven to 350°F. Place corn flour mixture in a pastry bag, and pipe into lightly greased regular madeleine pans or miniature madeleine pans, filling almost to top. Bake in preheated oven until golden brown around edges and centers spring back when touched, 5 to 6 minutes for miniature madeleines or 8 to 10 minutes for regular-size madeleines. Invert madeleines onto a wire rack, and let cool completely, about 10 minutes. Serve immediately.