Grate the zucchini on the fine side of a box grater. Bundle it in a clean kitchen towel and wring out as much liquid as possible over the sink. The zucchini should feel nearly dry when you are done. Set aside.

In a large bowl, beat the softened butter and 3/4 cup sugar together until pale and fluffy, about 2 minutes with a hand mixer. Add the egg and vanilla and mix until smooth.

Add the flour, cream of tartar, baking soda, and salt. Stir until a soft dough forms. Fold in the dry shredded zucchini until evenly mixed through the dough.

Cover the bowl and refrigerate the dough for 30 minutes. This keeps the cookies thick and rounded instead of flat, especially on a warm day.

Preheat your oven to 375 degrees F. Line two baking sheets with parchment paper. In a small shallow bowl, stir together the 3 tablespoons of sugar and 1 1/2 teaspoons of cinnamon.

Scoop tablespoon-sized portions of chilled dough and roll each one into a smooth ball between your palms. Roll each ball generously in the cinnamon sugar until coated on all sides.

Place the coated balls on the prepared baking sheets about 2 inches apart. Do not press them down. They will spread and settle on their own.

Bake for 10 to 12 minutes, until the edges are set and the tops have cracked and look dry. The centers may still look slightly soft, which is exactly what you want. They firm as they cool.

Cool on the baking sheet for 5 minutes before moving to a wire rack. Eat one warm if you can manage to wait that long.