Heat oven to 375°F; line sheets with parchment.
Cream butter and 1 cup sugar in a large bowl until fluffy. Beat in eggs one at a time, then vanilla.
Whisk flour, cream of tartar, baking soda, and salt separately; gradually mix into butter mixture until combined.
Mix remaining ½ cup sugar and cinnamon in a small bowl.
Divide dough into 30 equal portions; roll into 1½-inch balls and coat generously in cinnamon sugar.
Place 2 inches apart on sheets.
Bake 8-10 minutes until edges set and centers remain soft. Cookies puff, then flatten as they cool.
Cool on sheets 5 minutes, then on a rack. Store airtight up to 5 days.