Greenwood is best known as a chef, living and working in Washington, DC. Having trained in Paris as the first winner of the Anne Crutcher Fellowship from Les Dames d'Escoffier; she continued working in London, Paris, New York, San Francisco, Santa Fe and Key West before returning to her native Washington, DC. She has owned and cooked at her restaurants, Greenwood, Buck's Fishing & Camping, and Comet Ping Pong since 1996 and is well-known as one of the first DC chefs cooking in the currently fashionable style using seasonal and local ingredients. Her recipes and ideas, including coverage of both food and the food sculptures she has created in her restaurants, have been written about in the Washington Post, the New York Times, Gourmet, Food & Wine, as well as many other national & regional publications. During the Bush administration she became infamous for refusing to serve then Secretary of Defense, Donald Rumsfeld.

Greenwood was nominated for a James Beard Award in 2008. Greenwood graduated form The University of Richmond and studied at the Corcoran College of Art & Design. She has had solo exhibitions at Civilian Art Projects and Strand on Volta. Her work has been shown at the Corcoran Museum of Art as well as other galleries and venues in and around DC, and is held in many private collections.