Melt the white chips in the microwave using 50% power and stirring every 30 seconds. Set aside.
Beat the softened butter, the peanut butter and vanilla until well mixed, then add the melted chips and ½ cup of the powdered sugar. Continue adding powdered sugar until you've used the full 1 ½ cups. The dough should be thick enough to shape, but if it's not you can throw it in the refrigerator for a few minutes.
Shape into about 32 balls (see note). Put the balls on a parchment or wax paper lined tray or a couple of plates -- something you can fit in the freezer. Freeze the balls for about 30 minutes before dipping.
Melt chocolate in a microwave-safe bowl at 50% power, stirring every 30 to 60 seconds (60 is usually fine) or in the top of a double boiler. If using the microwave, you may want to melt just 4 oz at a time.
Using a toothpick, dip peanut butter balls partially into chocolate, keeping the top uncovered. Carefully transfer back to the parchment lined tray and put in the refrigerator to set the chocolate.
Notes
The peanut butter mixture starts out soft, so you'll end up having to chill it. I like to scoop out the 32 (or so) portions, chill, then shape the already chilled portions. If you can't work with the filling or find it's too soft and don't want to deal with chilling/freezing shenanigans, make these as peanut butter cups instead. Spoon melted chocolate into bottom of a mini or regular size muffin tins lined with cupcake papers. Flatten a portion of peanut butter filling and stick it in the middle, then cover with more melted chocolate. Freeze or chill until set. When cold, peel off the paper.