Possible Clues:

• ___ burger
• — burger
• Carrot or celery, informally
• Who might have struggle swallowing poultry product?
• Small carrot for those staying away from beastly types
• Fight over egg? One surely wouldn't
• Compete eagerly over cell for vegetarian
• ___ burger (meatless dish)
• Eater of no animal products
• Carrot or broccoli, briefly