Preheat oven to 350°F. Line an 8x8 square pan with parchment paper and butter generously.
In a microwavable bowl, melt butter and ¾ cup chocolate chips until melted and smooth. Stir in 30 second intervals. Stir in sugar, vanilla and espresso.
In a small bowl, whisk the eggs until bubbly on top, about 1 minute. Add the eggs to the chocolate mixture.
In another small bowl, sift together the flour, cocoa powder, baking powder and salt. Add the dry ingredients to the wet ingredients and mix until just combined and then add the remaining chocolate chips.
Spread half of the batter evenly into the pan. Place 16 Kit Kat pieces on top and the spread the remaining batter over it. Crush the 4 remaining Kit Kat pieces and sprinkle on top.
Bake for 35-40 minutes. A cake tester should come up with a couple of crumbs. Let cool and then cut into 9 squares.
Grease and line your pan with parchment paper so you can easily get the brownies out.