First up is Carter Green, the Vegetable Man of Oz, who first appears in The Hungry Tiger of Oz. He was a Winkie who pedaled fruits and vegetables throughout Oz, but eating too many of his own goods turned him into a vegetable himself. He is described as having a beet-like face with whiskers like roots, celery leaf hair, a turnip nose, corn ears, and a potato-ish body. In this form, he has no need to eat or sleep, but his feet will take root if he stays in one place for too long. His adventure occurred when Betsy Bobbin bought some strawberries from him, and the two of them were caught on one of those magical roads that were all over Ruth Plumly Thompson's Oz. They ended up in the country of Rash, where the Hungry Tiger had just arrived the previous night, and the three of them helped the rightful ruler of Rash, Prince Evered, to take back his throne from his evil uncle. While Carter is mentioned in some later books, he isn't really described as doing much of anything. March Laumer did write a book called The Vegetable Man of Oz, but the title character actually spends a lot of the story in an immobile form. I kind of have to wonder how Carter managed to stay alive, since Ozian plants don't share the near-immortality of the country's animals. He does replace his ears when they pop, so maybe he's gotten into the habit of growing replacement body parts for himself, as Jack Pumpkinhead does with his heads.
Following up the vegetable man with a medicine man, we come to Herby, a sort of Gillikin country doctor. Due to the general lack of sickness in Oz, many of Herby's medicines are designed to cure ailments such as bad tempers and yawning during speeches. Really, they're essentially mind- or behavior-altering drugs, which I know bothers some modern Oz fans, but maybe magic can overcome the harmful side effects that such drugs often have in the Great Outside World. Anyway, when Mombi became mad at Herby's using the best herbs in the area, she threw him into a cauldron of cough medicine and poured the resulting mess into a bottle. This bottle remained on a shelf until it was broken by Prince Philador of the Ozure Isles, which resulted in Herby's showing up again, just as good as new. Well, except he's shorter, has cough drops for eyes, and has a handy medicine chest inside his own chest. At the end of the story, Ozma appoints him as her Court Physician. As with Carter, he doesn't appear in any more major roles during the Famous Forty, but he's mentioned more often than the Vegetable Man. The late Mark Haas wrote a book with Herby as the star (called, sensibly enough, The Medicine Man of Oz), but it was pulled from publication due to copyright restrictions.