The same happened to me, but I did not use parchment paper to line the first two sheets I put into the oven. I did line the next two sheets with parchment paper and the cookies held up much better. I let the cookies cool slightly on the sheet before moving them to racks to cool completely.
Taste was really good-- I used Bob's Red Mill gluten free all purpose baking flour. The problem with the cookie was when I tried to remove from baking sheet it completely crumbled and would not hold together. Maybe someone out there can give me a suggestion, I am new at gluten free baking.