Preheat oven to 350F. Line or 2-3 spray baking sheets. In a medium bowl, whisk together flour, cocoa, baking soda, baking powder, cream of tartar, and salt. In a large bowl with electric mixer, cream together butter, sugar and powdered sugar until light and creamy, 2-3 minutes. Add oil and eggs and mix until well-combined. Add the dry ingredients and mix until dough comes together. It should be stiff, but not dry (and not overly wet or sticky).

Form dough into balls about the size of a golf ball or use a cookie scoop (about 3 Tbsp of dough per ball). Place the cookies several inches apart on the prepared baking sheet(s). Place 1/4 cup of sugar in a shallow dish.

Rub bottom of a flat-bottomed drinking glass lightly with butter or oil. Dip the glass into the sugar and press the glass onto a cookie, flattening to about 1/4-inch or slightly thicker. Repeat for all cookie dough balls.

Bake 8-9 minutes. Cookies will be very soft in the middle but set around the edges. Don't overbake. Cool a few minutes on the pan before transferring to a cooling rack to cool completely.

Frosting  With electric mixer, cream together butter and 1 cup powdered sugar until very light and fluffy, 1-2 minutes. Add remaining powered sugar, sifted cocoa powder, heavy cream, and vanilla. Mix 2-3 minutes until very thick and creamy. Spread frosting evenly on cookies. Decorate with sprinkles, if desired. Store well-covered in the refrigerator for 3-4 days.