In the bowl of a stand mixer, cream together the butter and sugar. Beat in the egg. Add the flour, baking soda, and baking powder. Mix well. Add in the potato chips, oats, peanuts and 3/4 cup white chocolate chips. Mix just until combined.
Place teapoons of dough on an ungreased cookie sheet. Bake at 375 degrees for 10 minutes. Allow the cookies to sit on the cookie sheet for 3 minutes, then move them to a wire rack to cool completely.
Melt the remaining 1/4 cup white chocolate chips in a microwave safe bowl. White chocolate burns easily. Melt this slowly, in 10-15 second intervals, stirring in between until just melted. Drizzle the melted chocolate over the cookies.
After the chocolate has set, store the cookies in an airtight container.
Notes
We did not refrigerate the cookie dough this time, although we have in the past for this recipe. If you like a thicker cookie without as much spread, refrigerate the dough for 30 minutes before baking.