Preheat oven to 400°F (200°C). Line 4 baking sheets with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter, 1¼ cups (250 grams) granulated sugar, and brown sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla.

In a medium bowl, whisk together flour, cream of tartar, baking soda, and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until combined.

In another medium bowl, stir together cinnamon and remaining ½ cup (100 grams) granulated sugar.

Using a 1½-tablespoon spring-loaded scoop, scoop dough (28 to 30 grams each), and roll into smooth 1½-inch balls. Toss in cinnamon sugar until well coated. Place 2 inches apart on prepared pans.

Bake, one batch at a time, until edges are lightly golden brown but centers still look slightly wet, 8 to 10 minutes. Let cool on pan for 5 minutes. Remove from pan, and let cool completely on wire racks.