In a large mixing bowl, combine room temperature (not melted) butter and sugar until smooth.
Add eggs and vanilla and combine.
In a separate bowl, sift together flour, cream of tartar, baking powder, and salt. This is an important step; you want to avoid lumps in your dough.
Slowly add dry ingredients into wet batter until fully incorporated.
Drop dough onto a large piece of saran wrap, mold it into a 4×4 square, and refrigerate for at least one hour. I often let mine sit overnight.
When ready to bake the cookies, generously flour a flat surface and roll out the dough. You can use as much flour as you need! I prefer to make cookies about 1/4? to 1/2? thick, but you can go thicker and still have successful results.
For best results, bake on silpat or parchment paper. You can reuse parchment, too!
Bake at 325-350 degrees for 5 to 8 minutes. In my oven, right about 6 minutes yields a perfectly cooked cookie, with no brown edges.