In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, peanut butter, and sugars together until light and fluffy, about 3-4 minutes. Add the vanilla and salt and continue mixing.
With the mixer on low speed, add the flour. Dough should cleanly pull away from the sides of the bowl when it's done. Set aside.
Line a baking sheet with wax paper. Melt 8 ounces of the white chocolate in the microwave until smooth, then spread the melted chocolate into a rectangle that's roughly 8"x12". Transfer to the refrigerator until hardened, about 5 minutes.
Once hardened, scoop cookie dough evenly over the chocolate and use a rubber spatula or your fingers to gently press the filling into an even layer.
Melt the remaining 8 ounces of chocolate in the microwave, then spread on top of the cookie dough. Immediately add the candy and sprinkles. Chill until set, about 20 minutes. Break into pieces and serve.