Line an 8x8" or 9x9" pan with foil and spray with nonstick cooking spray.
Place Oreo cookies in a food processor and pulse until roughly chopped. Reserve about 2 tablespoons of the cookie crumbs. Add the melted butter and blend until smooth, then add the powdered sugar and 3/4 cup peanut butter. Blend until thick. Press into prepared pan.
Place 2 tablespoons peanut butter and white chocolate chips in a microwave safe bowl. Heat on 50% power in 30 second increments, stirring between each, until melted and smooth. Spread over the mixture in the pan in an even layer and sprinkle with the reserved cookie crumbs. Chill until set.
For clean cuts, let the cold pan sit at room temperature for about 10 minutes and heat your knife under hot water. Use swift strokes when cutting and you'll avoid cracking the top too much. Store in an airtight container for up to 4 days.