In a world where sentient rabbits are the only living creatures, agriculture and cuisine are very different from our own—though perhaps not quite as much as one might think...
Diet
There are no animals besides succubuns in Burrowgatory—if there were, they would evolve intelligence in the same way that succubuns did, and be unsuitable to keep as livestock. Additionally, being descended from rabbits, succubuns are naturally herbivorous. These two facts have led to all food in Burrowgatory being strictly plant-based.
Fortunately, being so close to Hell, Burrowgatory has access to some very strange and fantastical plants. In addition to standard produce, Burrowgatory has "eggplants" that produce fruits unsettlingly similar in composition to eggs, "milkweed" that can be harvested to create pseudo-dairy, and all sorts of plant-based meat substitutes.
Agriculture
Thanks to the magical energies of Hell and the warm climate of Burrowgatory, agriculture has flourished. Crops grow very quickly with little risk of blight, and can be planted and harvested almost year-round. Thanks to this, Burrowgatory requires a relatively small number of farms and farmers to sustain its food supply.
While imps fill many of the roles that animals fill in the real world, they are not technically living creatures, and their bodies dissipate into nothingness if killed. Since they produce no by-products, they cannot be used as livestock. However, since they can be trained to eat all sorts of different things, many farms keep stables of imps to help with things like weed control.
Cuisine
Though Burrowgatory lacks the different cultures found throughout human civilization, their cuisines have been passed down to succubuns through the food demons feed them in their childhood. Any food found on Earth can be found in Burrowgatory (with plant-based substitutes for animal products), along with some more fantastical foods that succubuns have invented using the unique plants of Burrowgatory.