In a large mixing bowl, spoon the butter. Beat the chilled butter for 1 minute until smooth.
Add the sugars and beat well.
Pour in tahini then add egg and vanilla extract then beat to combine.
Add just one tablespoon of the milk and mix well, keep the other one if you feel the dough is not moist enough.
In another bowl, whisk flour, baking soda, and baking powder.
Add the flour mixture to the butter mixture and mix well. Note1
Cover with plastic wrap and refrigerate for 30 minutes or up to 3 days.
Preheat oven to 350F
Line a baking sheet with parchment paper.
Remove cookie dough from refrigerator and scoop batter into balls pressing lightly on sesame seeds if using.
Place cookies on the prepared baking sheet 2-3 inches apart. Cookies will spread. Note2
Bake anywhere from 8-10 minutes on the middle rack of your oven. Remove from oven when the edges are lightly brown and the middle is still pale.
Allow to firm up on the cookies sheet for a couple of minutes then transfer to a cooling rack.
Allow the cookie sheet to cool completely before adding another batch of cookies.