In a large glass measuring cup, melt ½ cup of butter
Use about 1 tablespoon to butter your Madeleine pan. Move the pan to the freezer to chill.
In a small bowl, combine the flour with the salt.
Using the whisk attachment of your stand mixer, beat the eggs and sugar on high until light and fluffy. Stop the mixer and add vanilla. Mix on low until just combined. Stop the mixer.
Add the dry ingredients to the egg and sugar mixture. Stir on low until the flour is just combined.
Keeping your mixer on low, slowly drizzle in the melted, cooled butter. Stir until the butter is mostly mixed in. Stop the mixer and fold the batter by hand 3-4 times until the butter is well mixed together. Be careful not to overmix.
Gently fold in ½ cup of mini chocolate chips
Cover batter with plastic wrap and chill for at least 1 hour. Batter can be saved overnight or for up to 2-3 days in the refrigerator.
Preheat the oven to 350°.
Once the oven is preheated, remove the cold pan from the freezer. Use your tablespoon cookie scoop (or two spoons) to add about 1 tablespoon of batter to each opening in the pan. Sprinkle each scoop with 5-10 mini chocolate chips.
Bake madeleines for 11-13 minutes. Begin checking madeleines for doneness at 11 minutes. The edges should be golden brown and the humps should bounce back a little when you gently poke them.
Allow madeleines to cool in the pan for 5-10 minutes. Carefully remove madeleines from the pan and move to a cooling rack to finish cooling.