Brush or rub the madeleine pan with a thin layer of ½ tablespoon softened butter. Dust with flour and tap out extra flour. Set aside.
In a medium bowl, whisk together the flour and baking powder. Set aside.
In a light-colored small pot over medium heat, melt the butter, stirring occasionally. Once the butter has melted, it will start to bubble and foam, stirring occasionally. Soon you will see the milk solids (white spots) at the bottom of the pan. Keep stirring. The butter and the milk solids will start to turn brown. It has a nutty aroma. Keep a close eye on the milk solids until they are just dark brown, but not black. The butter should be amber in color. Carefully transfer the butter to a small heatproof bowl. Measure out 6 tablespoons for use. Set aside and let it cool.
In a large mixing bowl, add sugar and eggs. Whisk vigorously for 1 minute. Add vanilla extract, salt and honey. Whisk until combined. Add flour and gently blend everything together. Finally, gently fold in the brown butter (6 tablespoons) a little at a time. Stir in the milk.
Fill the molds until almost all the way up to the edge. Use the back of a spoon to smooth the surface. Transfer to the fridge and chill for 2 – 3 hours.
Preheat the oven to 400˚F (204˚C). Place a large baking sheet in the oven while heating up. Carefully place the madeleine pan on the hot baking sheet. Bake for 10 – 12 minutes or until the madeleines are puffed and browned around the edges. The madeleines should spring back when pressed lightly in center. Remove from oven and tap out the madeleines. If needed, use a knife to help. Let them cool slightly before dipping in glaze.
For the glaze, in a medium bowl, add powdered sugar. Add the milk and 1 tablespoon water. Whisk until smooth. Add more water if the frosting is too thick. Add the rose extract and food coloring (if using), whisk again. Dipped the madeleines head in to get 1/3 covered. Lay them on a parchment paper to set, about 20 minutes. Serve as soon as possible.