Line a small plate with parchment paper. Scoop 14 level teaspoons of gluten free cookie butter spread, roll them quickly into small balls, and place on the parchment. Freeze for at least 1 hour until solid.
In a medium bowl, whisk together gluten free all-purpose flour blend, baking soda, cinnamon, and salt. Set aside.
In a large bowl, beat softened butter, brown sugar, and granulated sugar with an electric mixer until fluffy, about 3 minutes. Add the eggs one at a time, then beat in the vanilla extract.
Add the flour mixture and mix on low speed until a thick dough forms. Fold in the white chocolate chips. Refrigerate the dough for 30 minutes.
Preheat your oven to 350 degrees F and line two baking sheets with parchment paper. Scoop about 2 tablespoons of dough, flatten in your palm, place a frozen cookie butter ball in the center, and wrap the dough around it completely. Roll into a ball and place seam-side down on the baking sheet, spacing 3 inches apart.
Bake for 11 to 13 minutes until the edges are set and golden but the centers still look slightly underdone and puffy.
Let the cookies cool on the baking sheet for 8 minutes before transferring to a wire rack. The cookie butter center will be warm and gooey. Serve within a few hours for the best melty center.