Preheat oven to 350°F (175°C). Line baking sheet with parchment.
Cream butter and 3/4 cup sugar until light. Beat in egg, vanilla, and mashed banana.
Whisk flour, cream of tartar, baking soda, and salt; fold into wet ingredients until just combined.
Mix 2 tsp cinnamon with 2 tbsp sugar in a shallow bowl. Scoop 2-tablespoon portions and roll in cinnamon sugar.
Place 2 inches apart on sheet; flatten slightly with palm. Bake 10–12 minutes until edges set but centers still soft.
Cool on pan 5 minutes, then transfer to a rack to finish cooling.