As KRae said, it can take a long time. It's rather random and can appear early or late in the gardening career. Or not at all, even. It's just whatever the game decides to do. When they come, the opportunities should be like this:
Uncommonly Good - Bring in however many excellent pieces of produce specified. After completing this opportunity, your Gardener will be able to grow cheese and egg plants.
Outstandingly Rare - Bring in 10 excellent cheeses, Gardener will then be able to plant hamburger patties and steaks.
The Omnificent Plant - Bring in 10 outstanding steaks, Gardener will then be able to plant the Omni plant.
By knowing what the next opportunity will require, you can focus on getting that particular produce up to the high quality required.