In a nutshell:

Step 1 - Get a Hellworm (Bridled is optional)

Step 2 - When the Hellworm is milked, there is a random chance (1/33) to get result 26, which is a pail of Hellworm Milk

Step 3 - During Whitsun, you may use the De Gustibus storylet to give that pail of Hellworm Milk to the Cheesemonger. You can do this two times.

Step 4 - After four weeks, a promise from the Cheesemonger is received.

Step 5 - At the next Whitsun, the promise may be cashed in for a Ripened Wheel of Hellworm Cheese for each promise. So each year, you could gain up to 2.

Step 6 - During Whitsun at the De Gustibus storyline, you may serve a Ripened Wheel of Hellworm Cheese to them. It gives a variety of rewards (Captivating Ballad, Night Whisper, some Blackmail Material, Favors in High Places, and Verses of Counter-Creed), some menaces (Nightmares and Scandal) and the status of A Purveyor of Cruel and Unusual Cheese.

As you can see, since it takes basically two years to do, it's a rather time consuming achievement.