For thicker bars: prepare an 8×8″ pan by lining it with parchment paper. For thinner bars: prepare a 9×13″ pan. Set aside.
Make brown butter: in a medium-sized saucepan, melt butter over medium hear, stirring occasionally. Keep stirring until brown bits appear and butter smells nutty, several minutes.
Add peanut butter to pan and cook until melted and combined with the butter. Remove pan from heat and add in vanilla extract and confectioners’ sugar. Stir until smooth. Add in cereal and stir until evenly coated. Spread in parchment-lined pan and smooth out evenly.
In a double boiler or stainless bowl over a small pot of water (or in microwave), melt chocolate and coconut oil until smooth. Pour chocolate over peanut butter bars in pan. Let set in the fridge for an hour or until chocolate is hardened. Store in fridge.