When my son & I did cookie pops for Valentines Day we cut out hearts from rolled chocolate chip cookie dough, using the mini chips. We soaked popsicle sticks (or craft sticks) in a bowl of water for about an hour prior to baking, put an unbaked cut out on the cookie sheet, put a stick down, then covered it with another cut out. We had nice thick cookies and the sticks did just fine. I imagine if you are using drop cookie dough you could just slide the stick into the dough. I am not sure if this is the right way to do this, but it worked for me.