Make-ahead: The madeleines are best served warm, but they can be made up to 1 day ahead, cooled, and stored airtight at room temperature. Wrap them in foil and rewarm in a 350°F oven, if desired.
1. Position a rack in the center of the oven and preheat the oven to 350°F. Generously butter 7 molds of a large madeleine pan.2.
In a small bowl, whisk the flour and baking soda to blend. In a medium bowl, whisk the maple syrup, sour cream, sugar, eggs, and salt to blend. Stir in the flour mixture. Mix in the wheat bran, then mix in the melted butter.3.
Spoon about 1½ tablespoons of the batter into each of the 7 buttered molds. Bake for about 10 minutes, or until the madeleines are puffed and beginning to brown on the bottom. Immediately remove the madeleines from the pan and transfer to a cooling rack. Repeat to make the remaining madeleines, letting the pan cool and buttering it again before the second batch.4.
Serve the madeleines warm.