Measure the rice cereal into a large mixing bowl and set aside. Line a large baking sheet with parchment paper for cooling the finished puppy chow.

Combine the white chocolate chips and butter in a microwave-safe bowl. Microwave in 30-second intervals, stirring between each, until completely melted and smooth, about 1 to 1.5 minutes total.

Stir the vanilla extract into the melted white chocolate mixture until evenly combined. Pour the chocolate mixture over the cereal and gently fold with a rubber spatula until every piece is thoroughly coated.

Transfer the coated cereal to a large resealable plastic bag or a container with a tight-fitting lid. Add the powdered sugar, seal, and shake vigorously for 30 to 45 seconds until all pieces are evenly covered in a white coating.

Spread the mixture onto the prepared baking sheet in a single layer and let it cool for 5 minutes. Sprinkle the shredded coconut over the top and gently toss to distribute.

Allow the puppy chow to cool completely at room temperature for 10 to 15 minutes until the coating hardens. Break apart any large clusters before serving or storing.