1 cup butter, softened (2 sticks)
1 cup granulated sugar
2 whole eggs
½ cup plus two tablespoons whole milk, divided
1 teaspoon vanilla extract
1 tablespoon baking powder
4 cups all-purpose flour, or less
2 ½ cups sesame seeds, see Notes below
Place softened butter and sugar in the bowl of a mixer with paddle attachment and beat until smooth and pale, about one minute.
With mixer running on low, add one egg at a time. Scrape bowl and mix again.
Add two tablespoons of milk along with vanilla and mix just a few seconds to incorporate.
Add baking powder and mix.
With mixer running, gradually add flour until you have used 3 ½ cups. Check consistency of dough. It should be soft and pliable but not sticky. Use a little more flour as needed.
Use remaining flour to dust your counter and pour dough out onto flour and knead a few minutes, cover and let rest 15 minutes.
While dough is resting, preheat oven to 375 degrees F and place oven rack in top most position.
After resting, pour ½ cup of milk into a medium bowl and the sesame seeds into another.
Using a one-ounce scoop, scoop out 36 portions of dough onto your counter using all of the dough. Then roll each in between your palms to form 36 balls.
Line two cookie sheets with parchment paper.
Take one ball at a time and dip in milk then roll in the sesame seeds. Pick up the coated ball and form into a rectangle with your hands getting the height between half an inch and three quarters of an inch high and place on cookie sheet.
Repeat for all 36 balls and place on the two pans, 18 per sheet. They don’t rise or spread very much so they can be somewhat close together. I staggered the rows to fit 18 per pan with plenty of space between them.
Bake on top oven rack for 15 minutes, baking one pan at a time.
Use a spatula and slide them off onto a cooling rack that is sitting over a sheet pan to catch the sesame seeds that fall off.
Cool and serve.
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Club stores and some supermarkets often sell sesame seeds in larger 16-ounce containers or you can order them here.