Heat about 3 to 4 inches of oil over medium-low heat in a large potted fitted with a candy thermometer. You want the oil to be about 350 degrees, not higher.
Take the sheets of puff pastry (they will most likely be folded into thirds) and slice them on the seems. Each sheet will be cut into thirds. Once they are separate, brush one side of the cut piece with the beaten egg. Place a second piece on top of that, and brush it with beaten egg. Place the third piece on top. Gently press so they stick together. Repeat with remaining sheets – you should have 4 long rectangles now that have 3 sheets stacked in each.
Using a biscuit or doughnut cutter, cut holes in the stack. You will probably get 3 doughnuts from each (feel free to fry the scraps as they are also delish!). Cut a hole in the center – I actually use an apple corer for this part, but anything that can cut a hole right in the center will do.
Fry your doughnuts 2 to 3 at a time (no more as it will lower the oil temp) until they are golden and puffed, about 2 to 3 minutes each. Place on a paper towel to drain excess grease and repeat with remaining pastry.
For dipping, dip each doughnut in an alternating layer of dark chocolate, white chocolate and peanut butter. You can let the toppings set a bit before dipping each, but I like mixing them and getting that marble swirl look!
Serve immediately. These are best eaten right after frying!