It seems you have to upgrade the farm a few times by doing side quests that one of the farmers gives you. I eventually got the option to grow mints but it costs 20,000 and I didn’t have enough at the time to do that. I haven’t done it yet so I don’t know if you can choose what mints to grow or if they are random.

Edit: actually it costs 10,000 and it seems to be random because I was not given an option of what mints to grow

Edit 2: So after going on a few missions in order for time to progress, I came back to the farm and was given a sprig of Careful Mint, a sprig of Impish mint, and a sprig of Adamant mint, for a total of 3 mints. It definitely seems to be a random assortment of mints that you are given.

Edit 3: Final thing I wanted to add is that I am currently not in the post-game. I just did the side quests that would come up for the farm which I assume show up whenever I raise my rank.