Inner Cupboard Drawer
Option two is installing a cabinet organizer, which come in all sorts of configuration and materials and may be free-standing or attached to the interior of the cabinet. A web search for "pull-out cabinet organizer" stands a good chance of giving you some shopping direction.

Option one is consulting a local cabinet shop for suggestions and a quote. A custom solution is probably going to be price competitive with a high-end organizer while being exactly what you want rather than the inevitable compromises with premade solutions. At the same time you'll be able to explore all of your options, including replicating your current look on a cabinet with a drawer.