Preheat oven to 375°F.
In a small bowl, combine flour, baking soda, and salt, whisking to combine thoroughly.
In a small food processor (we use the smallest container in our Ninja set), combine chickpeas, oil, and butter. Process until smooth, scraping bottom and sides as necessary to make sure no chunky bits remain.
Transfer buttery chickpea mixture to a large bowl. Add sugar, peppermint, and vanilla. Use a hand mixer to beat until smooth. Add eggs one at a time, beating after each addition. Then, gradually beat in flour mixture in three or four additions. Beat just until thoroughly combined.
Stir in white chocolate chips.
Lightly grease your hands with cooking spray. Measure cookies out by rounded teaspoonfuls, shaping each measured cookie into a ball (you will probably need to re-grease your hands periodically). You should have 48 cookies. Place cookies on two parchment-lined cookie sheets (they won't spread very much at all, so they can be a little closer together than "typical" cookies).
Bake for 6-9 minutes, until puffed and just lightly golden brown. Do not over-bake – you will want to take them out of the oven a little bit before they seem completely set, or they will end up dry.
Immediately transfer cookies to cooling racks.
Nestlé brand chips: Throughout all our testing, we found that Ghirardelli brand white chocolate chips worked much better in this recipe that Nestlé. When shaping cookies into balls, the Nestlé chips don't adhere to the dough very well and sometimes fall out of the balls of dough, making the process of shaping your cookies much more difficult. If all you have on hand is Nestlé brand, you can make it work, but you will have to be a little more persistent in shaping the cookies. Alternately, if working with Nestlé chips, we recommend baking these as chickpea blondies (bar cookies) in a 9x9 pan instead.
Make-ahead and freezing tips: If you'll be storing these cookies for more than a day or two, they will stay fresher if tightly sealed or covered with plastic in the refrigerator. These cookies also freeze well – wrap them tightly in plastic and store them in air-tight zipper bags.