First it should be donated that Delicious in Dungeon is a comedic series, it still has a plot and drama and action but at its core it is a lighthearted series about a group of adventures exploring a dungeon and realizing they need to cook and eat the monsters they slay in order to do so, but for a long time it didn't have anything like this scene.
So, using some wiki help to do the heavy lifting, the elf is named Mithrun. Mithrun in the present is a completely hollow person, devoid of anything except the drive to kill demons.
Forty years prior to the start of the story, Mithrun joined and elvish group called the Canaries and as a result of this, a love passed him by. A mission brought Mithrun and his squad members to a port town to investigate what seemed to be a small, fairly harmless dungeon. In its depths, he came across a magic mirror that showed him a vision of his brother having a meal with the person he loved. Mad with rage, he smashed the mirror, and out from it appeared a small goat which offered him a life where he and his love were together as if he had not joined the Canaries. Mithrun desired this and accepted the goat's offer and in turn the goat became a genie like figure, giving Mithrun seemingly everything he wanted within the confines of the dungeon.
Initially, all was good and he lived a peaceful life with his friends and loved ones in a village in the dungeon. After a while, however, problems began to arise. As he tried to deal with these problems, the dungeon filled with more monsters and grew more complex, and the goat grew larger with each of his wishes. Eventually, Mithrun's friends disappeared, and he felt his vitality slowly slipping away. As he rested one night, the goat entered his chambers and started to devour him. Eventually he was found all alone in the decrepit dungeon with all of his feelings, wants, and desires eaten away. No hunger, no thirst, no lust, nothing...except hatred.
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