The Middleman will be the NPC on your left as you enter Ramsgate. He'll be dressed in armour, next to a shrine.
He'll give you a quest or two to teach you how to cook cells, and it's a process of waiting real-time (or spending money to speed up) to see if the cells you put in, come out in better rarity/condition.
For me, I just put an epic cell itself in there (purple colour) and some money. Let it cook for 2 days, then came back and got it out. The fact I cooked an epic cell to begin with, means I got an epic cell out in return, giving me this trophy.
You can cook 2 of the same cell-rarity/type together, to produce a higher rarity cell in return. Or you can just cook an epic cell with some money to turn it into another epic cell. Two greens make a blue. Two blues make an epic. An epic and some money makes an epic.