Beat 6 tablespoons of softened butter until creamy. Add 3/4 cup brown sugar and 1 1/2 tablespoons cinnamon; mix until smooth. Shape into marble-sized balls and place on a lined baking sheet. Freeze for 20 minutes or refrigerate for 1-2 hours until firm.
Preheat to 350°F. Prepare baking sheets with parchment paper or silicone mats.
In the same bowl, beat 1 cup butter until smooth. Add 1 2/3 cups sugar and beat until light and fluffy. Mix in 2 eggs and 2 teaspoons vanilla until smooth. Add 3 1/2 cups flour, 1 teaspoon baking soda, 3/4 teaspoon salt, and 1 1/2 teaspoons cream of tartar. Gently combine, being careful not to over-mix.
Fold in the frozen filling balls with a spatula.
Form 2-inch dough balls. Roll in a mixture of 1/3 cup sugar and 1 1/2 tablespoons cinnamon.
Place on prepared sheets, leaving 2 inches between each. Bake for 11-12 minutes. The edges should be firm but not golden, and the tops matte.
Immediately after baking, use spoons to gently reshape the cookies. Cool on the pan for 5 minutes, then transfer to a wire rack. Enjoy!