This is a simple quest. Snaf is just to the east of the main gate. It's obvious who he is as he wears an apron and constantly stirs a giant cauldron. As you approach be sure to take the upper path to avoid Mud (who is an annoying character who likes to tag along everywhere). You can deal with him later, but for now he's just an annoyance better avoided. Anyway, talk to Snaf. He gives you some Meatbug Ragout and tells you about the recipe, but says his previous errand boy never returned. Agree that it sounds great, and set off for the ingredients.
Head out the southern gate (just follow the path past Snaf's hut to reach it). Just over to the right you'll see a cave entrance with some Molerats (not Juvenile ones this time). Save here. Draw them away one by one and kill them, then go into the cave and search the corpse for an amulet inscribed NEK. This is crucial to another quest (Vanished Guard), but for now you might as well equip it and reap its benefits. Now search the surrounding area for Hell Mushrooms. There should be plenty. You'll also find some Slave's Bread. Snaf doesn't want that, but it has decent healing properties and has some trade value too.
If you killed all the Meatbugs on the way down from where you were thrown in you have enough Bugmeat already. Otherwise head to the ruined hut near the fallen tower (in turn near the southern gate) and kill the Meatbugs there. You can also knock Snaf down and loot his chest for some additional Bugmeat. Feel free to grab his weapon and loot his hut. As long as you don't kill him this has no effect on your disposition with him or anyone else and you can still complete the quest as if nothing happened.
When you have all the ingredients head back to Snaf. You can now collect a daily supply of three bowls of Meatbug Ragout from him, making him a permanent food source.