Art of making delicate French butter cookies (Madeleines)
If they're cooking too fast that they're browning and fully cooked through after 10 minutes instead of the recommended 14... that's probably a signal that you should turn the oven temperature down.

If you don't already have an oven thermometer, get one. It's possible for ovens' internal thermostat to be significantly off - by 50 degrees or more at times. Rather than depending on it, you will be better served by having a thermometer. These are generally inexpensive and can be found at most kitchen stores or on the web. 

If you find that your thermostat is off, look into how to reset it, or learn the offset and add/subtract that amount from the dial temperature. If it's not off, try dropping the temperature by 25 F to start. The recommended oven temp seems to vary based on the recipe... from between 350 to 400 F. One thing that the 400 F recipe does is they place a cookie sheet under the madeleine pan, which may protect the underside somewhat.



Another possibility - you don't show your madeleine pans but to reduce browning, it's generally recommended to use very light colored pans. From Serious Eats:


  If you want foods to brown on the bottom, reach for a darker metal sheet pan because dark pans will absorb more heat and therefore more heat will radiate off the surface. I like to use dark pans when I'm baking pizza or crispy-edged potato wedges and roasted veggies that I want to brown. Recently, I've even started baking pies in dark metal pie plates instead of glass so the bottom of the pie crust heats up more and browns.