Combine dry ingredients. Combine the GF flour, cream of tartar, baking soda, salt, and butter in a medium bowl; whisk to blend thoroughly.

Make the cookie dough. In a large mixing bowl with an electric mixer, beat the butter with the 1 1/2 cups of granulated sugar until fluffy and pale in color, about 3 minutes. Add the eggs and vanilla and blend well. Add the dry mixture to the mixing bowl and stir until blended. Chill for about 20 to 30 minutes.

Prep the oven and pan. Heat the oven to 375°F and line baking sheets with parchment paper.

Shape and coat the cookies. Shape the chilled dough into small balls, about 1 inch in diameter, and roll them in the cinnamon-sugar. Arrange them on the baking sheet, leaving about 2 1/2 inches between them. They will spread, but if they're chilled they shouldn't spread too thinly. You could even shape and roll them and stick the baking sheet in the freezer for a few minutes.

Bake. Bake the snickerdoodles for about 10 minutes, or until they look set and sink slightly in the centers.