To acquire the cheese for the banquet, you need to help Brayflox rid the Longstop of the foes that have overrun it.
How to Unlock
Brayflox's Longstop is unlocked by the level 32 Main Scenario Quest The Things We Do for Cheese.
Meet a Longstop Ally
Go northwest to find a Goblin Pathfinder. Talk to them to receive the Runstop Headgate key.
Access Brayflox's Runstop
Go east to the Runstop Headgate and check on it to unlock it with the key.
Great Yellow Pelican
Beyond the gate, you are attacked by a Great Yellow Pelican and three Violet Backs. Kill the Violet Backs first. They will use Poison Breath repeatedly. Eventually, the Pelican will start using Numbing Breath, a cone attack that inflicts Paralysis. Avoid standing in it. Kill any additional ziz that appear (e.g. Sable Back, which uses Slumber Breath; Blue Back, which uses Petribreath; Violet Back, which uses Poison Breath), then resume attacks on the Great Yellow Pelican until it dies.
Access Mudstop Watergush
Go north and the Goblin Pathfinder will follow. If you can kill the Mud Biast and Comet Chasers before they can kill the Goblin Pathfinder, you will get an extra treasure coffer.
There are optional areas, which most players will want to skip, where you can get bonus treasure chests by killing enemies before they can kill other Goblin Pathfinders. One of these areas is to the north, and one is to the south, and one is up a ramp to the southwest.
Go to the area to the west to reach another dungeon boss.
Inferno Drake
After you reduce Inferno Drake's health by a certain amount, a Tempest Biast will appear, and will chase Brayflox Alltalks around the area. Focus your attacks on the Tempest Biast until it dies. The Inferno Drake will periodically cast Burning Cyclone, which will hit everyone in front of it, including Brayflox if she is in its path. When the Inferno Drake and Tempest Biast have been defeated, the gate to the next area will open.
Arrive in the Heart of the Longstop
After you go through the tunnel beyond the gate that opened, you will reach a large open area with many enemies. You can stay along the left wall to minimize the number of enemies that attack you.
Hellbender
Hellbender will target random players with Bog Bubble, which does damage in a circular area around the player. It will also cast Peculiar Light, a circle attack centered on itself, which inflicts a Magic Vulnerability Up status, and a cone attack called Stagnant Spray.
After you deal a certain amount of damage, it will start using Effluvium, which traps a random player in a Queer Bubble. The player inside can still use combat actions. Players should target the Queer Bubble to free the trapped player.
Eventually, Aiatar will descend from the sky and kill Hellbender before flying away. Wait a few moments and the gate to the next area will open. Go to the end of the tunnel and check on the Longstop Gutgate to open it.
Defeat Aiatar
The dungeon boss is in the northernmost area on the map. There are various dead ends in the area before it that you can ignore, as they do not contain treasure chests.
Aiatar
Aiatar will use Dragon Breath, a line attack that inflicts a stacking Poison status. The more times a player is hit with this, the higher the number of poison stacks they will get, causing them to take damage over time at a faster rate. The Healer should use Esuna to remove the poison. Aiatar will also sometimes hit the tank (or whichever player has enmity) with Salivous Snap, which also inflicts a stacking Poison status.
Eventually, Aiatar will start casting Toxic Vomit, which creates a poison puddle on the floor. If Aiatar stands in the poison, it will gain health over time. The tank should try to move Aiatar away from the poison. In the Chat Log settings (click the ⚙️ to the right of the chat tab names), you can choose one of the Log Filters and go to the Battle tab, then select "Engaged Enemy" from the dropdown, and check "Beneficial effects granted to engaged enemies" and "Beneficial effects on engaged enemies ending" to display "Aiatar gains the effect of Rehabilitation" when it is standing in a poison puddle, and "Aiatar loses the effect of Rehabilitation" when it is no longer standing in a poison puddle.
Players who stand in the poison puddle will get the Pollen status, but they can remove the status by not standing in the puddle.
Eventually, Aiatar will start occasionally using Granite Rain, which causes damage to all players.
Completing the Quest
Defeating Aiatar will complete one of the quest objectives for the Main Scenario Quest The Things We Do for Cheese.