Step 1: In a large bowl or the bowl of a stand mixer, cream together the softened unsalted butter and 1 1/2 cups granulated sugar on medium speed until light and fluffy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
Step 2: Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract until just combined.
Step 3: In a separate medium bowl, whisk together the all-purpose flour, baking soda, cream of tartar, and salt.
Step 4: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix the dough.
Step 5: Cover the dough tightly with plastic wrap and refrigerate for at least 30 minutes, or up to 2 hours. This chilling helps prevent spreading.
Step 6: Preheat your oven to 375°F (190°C). Line baking sheets with parchment paper. Place about 1/2 cup of extra granulated sugar in a shallow dish for rolling.
Step 7: Scoop generous tablespoons of chilled dough and roll each into a ball. Then, roll each dough ball in the granulated sugar until fully coated. Place the sugared dough balls about 2 inches apart on the prepared baking sheets.
Step 8: Bake for 8-10 minutes, or until the edges are lightly golden and the centers are still slightly soft and puffy. Do not overbake. The cookies will firm up as they cool.
Step 9: Remove from the oven and let cool on the baking sheet for 2-3 minutes before transferring to a wire rack to cool completely.