Pre-heat oven to 375°F and line a few baking sheets with parchment paper. (I bake them at 350°F in a convection oven)
In a large bowl, whisk together the flour, baking soda, and cream of tartar. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, oil, and sugars on medium-high speed until light and fluffy, scraping the sides as necessary.
Reduce speed to medium and add the egg (or your egg substitute), mixing just until combined.
Add the vanilla and mix until combined.
Reduce speed to low and add the flour in three additions, scraping down the sides as necessary.
Using a scoop that holds 2 tablespoons of dough, drop batter onto the baking sheet, spacing at least an inch apart.
Bake for 8 to 10 minutes, just until the edges begin to darken.
Let cool on baking sheet.