Cream the butter and sugar: In a mixing bowl, beat 1/2 cup softened unsalted butter with 3/4 cup granulated sugar until light and fluffy, about 2 minutes.
Add egg and vanilla: Beat in 1 large egg and 1 teaspoon vanilla extract until smooth and well combined.
Whisk dry ingredients: In a separate bowl, whisk 1 1/2 cups all-purpose flour, 1 teaspoon cream of tartar, 1/2 teaspoon baking soda, and 1/4 teaspoon salt.
Combine: Add dry ingredients to the wet mixture. Mix on low until a soft dough forms. If crumbly, add up to 1 teaspoon milk. The dough should be soft but not sticky.
Chill (recommended): Cover and chill the dough for 20–30 minutes. This helps the cookies keep their shape in the air fryer.
Make the coating: Stir 1/4 cup sugar with 1 1/2 teaspoons cinnamon in a small bowl.
Form balls: Scoop tablespoon-sized portions and roll into 1 to 1 1/4-inch balls. Roll each in cinnamon sugar to coat generously.
Prep the air fryer: Preheat to 320°F (160°C) for 2–3 minutes. Line the basket with parchment or a perforated liner. Avoid wax paper.
Arrange: Place coated dough balls in the basket, leaving 2 inches between them. Gently press each ball to about 1/2-inch thick for even cooking.
Air fry: Cook at 320°F for 6–8 minutes. Cookies should be set at the edges and soft in the center. They will firm up as they cool.
Cool: Let cookies rest in the basket for 2 minutes, then transfer to a rack to cool completely.
Repeat: Continue with remaining dough. If your kitchen is warm, keep unbaked dough in the fridge between batches.