In a medium bowl, combine the flour and salt with a wire whisk.
In a stand mixer, cream the butter and sugar together. Add the eggs and vanilla and beat on medium speed until mixed well.
Scrape down the sides of the bowl and add the flour mixture.
Mix just until combined, being careful not to overmix.
Divide the dough in half, gently flatten the ball into a disk and wrap tightly in plastic wrap.
Refrigerate for 1 hour.
On a floured surface, roll out the dough to 3/8" thick. Use a 4" circle cutter and cut as many circles as possible, re-rolling the dough scraps and cutting again.
Place the circles on a non-stick baking sheet.
To press the lollipop sticks into the cookie, gently place your hand on top of the circle. Push the stick about 1- 1 1/2" into the circle, being careful that the circle does not misshapen.
Refrigerate the cookie dough for another hour.
Preheat the oven to 325 degrees.
Bake the cookies for 12-13 minutes, pulling the cookies out just before they start to brown.
Immediately transfer the cookies to a flat surface to cool.
Once the cookies are cooled, decorate as described in the blog post above.
Notes
*The amount of cookies you get will greatly depend on how thick you roll the dough and how large your cookie cutter is. I'd say you'll get anywhere from 3-5 dozen cookies with this recipe depending on those factors.