Coat a 10-inch cast iron skillet with some of the melted butter using a pastry brush. Set aside.
For the dough, whisk the flour, baking soda, cream of tartar, and salt together in a large mixing bowl. In a separate medium bowl, mix together the remaining melted butter, granulated sugar, brown sugar, and egg. Pour the liquid mixture into the flour mixture. Beat together using a hand mixer on low speed until combined. Let the dough rest uncovered for 10 minutes, or until firmed and not sticky.
Meanwhile, make the chai spice coating. Stir together the granulated sugar and all of the ground spices in large bowl. When the dough is firm, gather it together with your hands and form into a large ball. Roll the ball in the spices repeatedly until the ball is totally covered with the sugar and spice mixture. You will have leftover chai spice (save for other use).
Place the ball in the center of the buttered skillet; do not spread or flatten it. The ball will spread as it bakes. Bake for 35 minutes, or until the cookie fills the pan and is golden brown and crackled on top. Cut into wedges and serve warm with scoops of ice cream and leftover chai spice sprinkled on top. Or store room temperature wedges in an airtight container for up to 4 days.