These biscuit-like cookies are addictive! Such crunchy texture and nutty sesame flavor. Keep the cookies dry by storing them, immediately after cooling, in an airtight container. They’ll last several weeks that way. The dough is best used to shape and bake the cookies right after it’s made.
Place oven rack in the middle of the oven, and preheat the oven to 375˚F. Line two heavy duty sheet pans with parchment paper. In a small bowl, whisk together the flour, cream of tartar, baking soda and salt.
Using a stand mixer fitted with the paddle attachment, or a hand mixer, beat the soft butter with the sugar on high speed until well combined and fluffy, about 2 minutes. Add the egg and vanilla and beat on medium speed until combined.
Slowly add the flour mixture and beat slowly on low speed, then increase the speed to medium and beat until the mixture comes together. The dough will be very dry and still showing flour. Add the milk and beat until a soft dough forms.
Place sesame seeds in a small bowl. Shape about a tablespoon of dough into a ball and flatten to about ¼-inch disk, Press the disk into the sesame seeds, turning over and onto its sides to coat completely with sesame seeds. Repeat with the rest of the dough and sesame seeds. Place the cookies about an inch apart on the sheet pan, baking the first pan as soon as it is ready and continuing to make the second pan of cookies while the first one bakes.
Bake the cookies for 14-16 minutes, until golden brown, rotating the pan halfway through baking for evenness. Remove the pan from the oven and cool the cookies completely; they will firm up and get crunchy when they are cool. Store immediately in an airtight container.