Preheat oven to 350°. Line a 8x8 baking pan with parchment paper and set aside.
In a microwave safe bowl, heat butter in microwave until completely melted. With a spoon, stir in brown sugar until smooth. Add in egg and vanilla until combined. Incorporate the flour and mix until just combined. Spread half of the mixture into prepared baking pan and make sure top is level. Place kit kats on top. I made a square border around the pan (leave room around the edges for the batter to fill around them) and then placed the rest in straight lines filling the square in one direction. If they all don't line up, that's okay it won't make a difference. Once the kit kats are where you want them, press down a bit so they stay in place better when smoothing the second half of batter on top.
Start spreading the rest of the batter on top. Do this in small sections as the batter is very thick and it makes it much easier spreading it in bits and pieces. Make sure to cover all kit kat areas and around the edges where you left room.
Place in preheated oven and bake for 25-27 minutes. (Mine were done in 26 minutes.) They will appear to be not done, but they will firm up as they cool and be nice and chewy. Once done, let them cool in pan for about 10 minutes. Pul them out by the parchment paper hanging over the sides and let them cool another 10 minutes. Cut them up into bars and enjoy!