Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper.
In a large bowl, beat the softened butter and granulated sugar until creamy and well blended.
Add the eggs one at a time, mixing well after each addition. Beat in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, cream of tartar, and salt
Gradually add the dry ingredients to the butter mixture. Mix just until a soft cookie dough forms. Avoid overmixing.
Gradually add the dry ingredients to the butter mixture. Mix just until a soft cookie dough forms. Avoid overmixing.
Refrigerate the shaped dough for at least 30 minutes. For thicker cookies with better texture, chilling for closer to 60 minutes is even better.
Bake for 10 to 12 minutes, or until the edges are lightly golden while the centers still look soft.
Let the cookies cool on the baking sheet for about 5 minutes before transferring them to a wire rack.