In a large bowl (or using a stand mixer, hand mixer, or by hand), cream together the sugars and butter until light and fluffy, about 3 minutes.
Add the eggs and vanilla, and beat for another minute.
Sprinkle the flour on top of the butter mixture, and then sprinkle the baking soda, cream of tartar, and salt on top of the flour. Mix until well combined. The dough will be tacky but not overly sticky.
Form into long logs, wrap in wax paper, twist the ends to close, and refrigerate until firm or you are ready to bake. I like to make three logs that are about 2 inches in diameter.
When you are ready to bake cookies, slice 1/2-inch thick slices off the cookie dough log and place them on a parchment lined baking sheet. Bake at 350 degrees F. for 8 to 11 minutes. Store unused dough in the fridge until you are ready for another round of hot cookies.
Notes
The diameter of the log will determine the size of the baked cookie. A circle around 2 inches across makes a nice-sized cookie when sliced and baked.
This dough has lasted over two weeks in my fridge before. To keep the dough from drying out, I usually wrap the logs in plastic wrap in addition to the waxed paper.
I love having dough on hand. One morning, I sent a bag of hot cookies to my neighbor after he brought my chickens back home. They had wandered into his yard and couldn't figure out how to get home. I also used them as a quick dessert when I made dinner for a family from church. You'll love having this delicious dough on hand!
This is a large batch. You can either halve the recipe or store half the dough in the freezer. Thaw in the fridge before baking.