In a large bowl, with an electric stand or hand mixer, beat butter and sugars for 2-3 minutes until light and fluffy. Then add tahini and beat until smooth.
Then mix in flour and salt just until combined (on low speed or with a large spoon).
Divide dough into two equal-ish pieces and place each on a large piece of parchment paper. Use the parchment paper to form each piece into a log, about 1- 1.5 inches in diameter.
Roll up each log in the parchment paper and secure the ends by twisting. Refrigerate for 2 hours minimum or overnight.
When ready to bake, pre-heat the oven to 325 degrees F.
Brush each log with egg white and roll in sprinkles or sprinkle them on (is that why they are called that?!?). My kitchen is hot (Puerto Rico problems) so I stuck the logs in the freezer for 10 minutes or so after rolling in sprinkles.
Line 2 cookies sheets with parchment paper.
Slice each chilled log into 1/4 inch discs and place on the parchment lined cookies sheets at least one inch apart. Bake for 15 minutes or until the cookies just start to brown on the bottoms. They will harden as they cool. Cool completely on cookie sheets and eat! Store in an airtight container at room temperature for up to 5 days.