Using a stand mixer, cream butter until fluffy.
Add sugar and cream together.
Add vanilla extract and cream together on low.
Slowly add rice flour and all purpose flour to the butter mixture. Mix together until almost fully combined. Remove dough from stand mixer and turn onto the countertop.
Form the dough into a ball as best as you can. Cover with cling wrap and refrigerate the dough for 30 minutes.
Roll the dough out, be patient as this takes a bit of time. Roll the dough until it's 1/4" in thickness.
Use cookie cutters to cut the dough into shapes.
Place the shortbread cookies on a baking pan (ungreased). Prick the cookies with a fork. Bake shortbread cookies for 15-18 minutes at 300 degrees F. When the cookies are finished, they should be light, white colored. If the edges have begun to turn brown, they are overbaked.
Cool on the baking pan for 5 minutes, then gently place them on a cooling rack.
Store cookies in an airtight container for up to 4 weeks.