What are the most sustainable options for cooking "appliances." Obviously any appliance or cooking device that utilizes petroleum-based gas to fuel their heat source is going to be unsustainable. But what are the best options that are sustainable?
If you live remotely, and have lots of wood or other biomass growing out back that you can harvest by hand, and that will grow at least as fast as you harvest it, then that is probably the most sustainable cooking fuel. However, this sort of cooking is typically 30-40% efficient, so high inputs are needed for a given output.
For everyone else, then induction hobs, well-insulated convection ovens and microwave ovens powered by electricity generated from renewable sources are the most sustainable cooking media, as long as the cooking devices are sent for repair or recycling at the end of their lives.
As usual, a life-cycle assessment database would be needed to assess the full cradle-to-cradle impact of particular devices. Publications such as Ethical Consumer do audits, including sustainability, of various consumer devices including cookers. Espresso fans like me will be reassured to see that the classic Bialetti stove-top scores well on sustainability (if you can live with having that much steel or aluminium dedicated to a single wonderful purpose.)