Spread butter in a 9x13" pan, or spray with cooking spray. For easy cleanup, you can line it with foil or parchment paper first.
In a large glass bowl, combine the white chocolate and peanut butter. Melt in the microwave at 50% power, stirring every 30 seconds.
Stir the marshmallows into the peanut butter mixture and let cool for 4-5 minutes. Stirring often will speed up the process.
Add the rice crispies, then the mini chocolate chips. Stir until well coated.
Press the cereal mixture gently into the prepared pan. If desired, sprinkle remaining chocolate chips on top and press them into the bars so they stick. (You can also press extra marshmallows on top of you want.)
Chill the bars for 20-30 minutes, or let them sit at room temperature for 2 hours, or until set.
Cut into squares and serve. The bars are quite rich, so I cut them into small pieces, but you can cut larger squares if you prefer.
Notes
The chocolate chips will melt if your white chocolate mixture is too warm, so make sure you let it cool. You can test it by adding a couple of chocolate chips. If they melt, let it cool awhile longer.
If you use creamy peanut butter, you will only need a scant 2/3 cup.
Store the bars in an airtight container for up to a week. I like to place wax paper between the layers.