Beat the butter and 1 cup (221g) of the sugar in the bowl of a stand mixer 2 minutes or until light and fluffy. Add eggs, one at a time, beating well after each addition. Scrape down the bowl and beat in the vanilla bean paste.
Whisk flour, baking soda, cream of tartar, and salt in a separate large bowl. Gradually beat into butter mixture until fully combined (I do this in 2 additions), being careful to not overmix.
Cover the cookie dough and chill at least 2 hours or up to 2 days.
Preheat oven to 375°F. Add remaining 1/2 cup sugar to a small shallow bowl.
Roll cookie dough into 1-inch balls, drop in sugar and roll to evenly coat. Place cookie dough balls on a parchment paper-lined baking sheets about 2 inches apart.
Use the bottom of a glass to gently press down on each cookie dough ball (they don't spread very much in the oven so they need a little bit of help on the front end).
Bake 10 to 12 minutes or until edges are just slightly golden brown; cool 2 minutes on pans before moving to cool completely on wire racks.
You can store these cookies at room temperature in an airtight container or plastic bag for up to 3 days.