Heat oven to 325°F. Coat 4 (6-ounce) ramekins with butter and sprinkle the insides with sugar. Bring a kettle of water to a boil while you prepare the batter.
Whisk together the flour, cocoa, baking powder, and salt. Set aside
Puree the butter, sugar, and eggs in a blender for 1 minute.
Add the milk and vanilla extract to a microwave-safe bowl. Microwave on high until warm, about 30 seconds. Add the instant espresso powder and stir until dissolved.
Add half of the flour mixture to the butter mixture in the blender and puree for 30 seconds. Add the milk mixture and puree again for 30 seconds. Add the remaining flour and puree for 1 minute.
Divide batter evenly among prepared ramekins.
Set the ramekins in an 8-inch square pan and set the pan on the oven rack. Pour hot water into the pan, about 1/8 inch deep. Slide the rack with the pan into the oven and bake until a toothpick inserted comes out clean, 45 to 50 minutes.
Remove pans from oven and let ramekins stand in water for 5 minutes.
Remove ramekins from water and cool slightly before serving. The soufflés can be served straight from the cups or inverted onto a plate.