Preheat oven to 350 degrees. Lightly grease 9x13 inch pan.
Melt butter in microwave-safe bowl or in saucepan over low heat. Add sugar and stir to combine.
Return mixture to heat briefly until it's hot and starting to bubble (this allows the sugar to dissolve, which will yield a shiny top crust).
Stir in cocoa, baking powder, salt, espresso powder, and vanilla. Cool until you can test with finger and mixture feels like comfortably hot bath water.
Mix in applesauce.
Whisk in eggs, stir until smooth, then add the flour and chips, again stirring until smooth. Spoon batter into prepared pan.
Bake until sharp knife or cake tester poked in middle reveals wet crumbs but not raw batter, 30 minutes. The brownies should feel set on edges and in the center. Remove from oven and cool on rack, cover when cool. Let sit overnight before serving to allow the bran to soften.