In the bowl of a stand mixer, add the butter, sugars and salt. WIth the paddle attachment, cream the butter on medium speed until it pales in color and becomes a little fluffy.
Add the vanilla and mix for a few seconds.
Then add half the flour and pulse on low speed for just a few seconds, scraping down the sides periodically until slightly incorporated. Then add the rest of the flour and mix until almost fully combined. (You will yield a nice and tender cookie if you don't over mix the dough.) Use your spatula to gently incorporate any loose flour.
Dump the dough out onto a clean sheet of parchment paper. And form into a log.
Cut the log in half. Pour half the sprinkles out onto the parchment and roll both logs in the sprinkles until mostly covered, using more sprinkles as necessary.
Place the logs side by side again and roll up snugly in the parchment. Place in the refrigerator for an hour or wrap the parchment in plastic wrap and place in the freezer for longer storage.
To bake, preheat the oven to 325F/ 162C. Line a baking sheet with parchment paper and remove the log from the fridge. (if frozen, let defrost on the counter a bit.)
Using a large, sharp knife (not serrated) slice the dough into rounds, just under 1/2" thick and place on the parchment-lined pan. Add a few more sprinkles where necessary if desired. (If they don't slice easily, wait a few minutes for the dough to soften just a tad.)
Bake for about 20-25 minutes until just golden, rotating the pan halfway through baking, Remove and let cool on the pan for about 5 minutes before carefully transferring the cookies to a wire rack to completely cool.
Store the baked cookies in an airtight container for up to a week
*The frozen logs of dough can be wrapped tightly and kept in the freezer for a few months.
*Adding lemon or orange zest can give the cookies a nice citrus note, but will be visible on the surfaces.