Preheat oven to 350 degrees and position rack in middle of oven. Spray madeleine pan with nonstick cooking spray.
In a medium bowl, whisk together flour, baking powder and salt. Set aside, In a small bowl, whisk together espresso powder and hot water to make a paste.
Combine butter and sugar in a microwavable bowl. Microwave on low power for 1-2 minutes. Whisk until smooth. Continue microwaving in 15 second intervals until butter is totally melted and mixture is smooth.
Let mixture cool for 3-4 minutes.. Add eggs, one at a time, whisking after each addition.
Add milk until well combines. Next, add flour mixture, whisking until well combined.
Stir in espresso mixture and then fold in chocolate chips.
Using a 1 1/2 inch diameter scoop or a teaspoon, fill molds until almost full. Press batter to evenly distribute.
Bake for 10-12 minutes, until the madeleines are puffy and the tops spring back when gently pressed. Do not overbake.
Remove from oven to cool on rack for 2-3 minutes. Use offset spatula to remove from pan.