Preheat oven to 450F.

Mix together shredded zucchini and salt and set aside.

Pulse the flour, baking powder, and baking soda in the bowl of a food processor. Add the butter and process until the mixture resembles coarse cornmeal and there are no large lumps of butter left, about 6 1-second pulses. Add the cheddar and herbs and pulse once or twice to combine.

Add the buttermilk and pulse a few times, until the dough gathers into clumps. Scrape the biscuit dough into a large bowl.

Wrap the zucchini in a cloth or paper towel and squeeze it to remove all the water. Once you have squeezed out all the water you can, add it to the dough, mix it in, and form the dough into a rough ball.

Divide the dough into 12 portions and lightly shape them into balls. Place the biscuits on cookie sheets, 6 biscuits per sheet. Bake for 10 minutes.