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Outside of your restaurant to the upper right, there is a big patch of dirt. When you first start out, you won't be able to plant anything, but as you level, you'll unlock up to nine spots where you can plant seeds for 2,000 coins each. These seeds sprout and grow as you water them, and are ready to harvest in 48 watered hours. Nothing bad happens if they go dry; they just stop growing until someone waters them.
It's random which Restaurant City ingredients sprout, and not every ingredient can be grown in the garden. Among those that can are basil, oregano, coriander, garlic, bay leaves, tea, coffee, vanilla, sugar, saffron, wasabi, mint, and ginger. New ones show up in the garden as new ingredients are introduced to the game.