Preheat the oven. Set oven to 390°F (200°C).
Mix wet ingredients. In a bowl, combine egg, salt, vanilla extract, sugar, honey, and milk. Mix until smooth.
1 medium egg, 1/8 tsp salt, 1/2 tsp vanilla extract, 1.5 oz sugar, 1 tsp honey, 1 tbsp milk
Add dry ingredients. Sift in flour and baking powder, then mix until incorporated.
2 oz cake flour, 1/4 tsp baking powder
Add brown butter. Pour warm (not hot) brown butter into the batter, stirring until smooth.
4 1/3 tbsp brown butter
Prepare the pan. Grease the madeleine molds with butter and, if necessary, dust with flour.
Fill and bake. Fill molds 3/4 full, bake at 360°F (180°C) for 9-10 minutes, until golden brown.
Cool. Let them sit for a couple of minutes, then release from the pan.