Place all Thin Mints in a plastic bag, place bag between a kitchen towel, and coarsely crush cookies using the flat bottom of a pan or a rolling pin. Divide the crushed cookies in half and set aside.
In a separate large bowl, cream together butter and sugar, by hand or with a mixer. Gradually add eggs, one at a time, then add vanilla extract and white chocolate chips. Mix well.
In another large bowl, mix together flour, baking powder, and salt. Gradually add flour mixture to butter mixture, mixing well, until dough is slightly stiff but still soft. Gently mix in one half of the reserved crushed Thin Mints into the dough.
Turn out dough onto a lightly floured surface and form into two small rectangular loaves. Place on a large baking sheet lined with parchment paper or a silicon baking mat and bake for 20 minutes. Let cool on sheet for 5 minutes.
Reduce oven to 300F/148C degrees. Remove biscotti loaves from pan and cut into 1/2-3/4" slices on the diagonal with a sharp knife and place slices on baking sheet. Bake for additional 15-20 minutes.
Transfer biscotti to wire rack and let cool completely. Dip one end of each slice into the melted white chocolate and roll in the remaining crushed Thin Mints. Place back on the wire rack to dry.
Store in an airtight container 4-6 weeks (if they last that long!)