Begin by cutting all of the rinds off of the Green Hills. Once the rinds have been removed, cube the rest (paste) of the cheese.
Place the cubed Green Hill into a food processor and start blending at medium speed. After a couple of minutes, scrape the side of the processor. The cheese will be stiff and sticky.
Continue to whip the cheese, turning the speed up from medium to high. Be sure to scrape down the sides of the processor every couple of minutes. Continue to whip the Green Hill until it gets lighter in texture. Once the Green Hill is soft and similar in texture to whipped butter, stop whipping it.
Fold in the fresh thyme to whipped Green Hill. Transfer the whipped Green Hill into a serving bowl.
Add a piece of honeycomb to the center of the whipped Green Hill and enjoy!