Possible Clues:

• Muppet with quite an appetite
• Dessert fiend on 'Sesame Street'
• TV character who once fantasized about eating the moon because it resembled his favorite snack (Alaska)
• Muppet with a major sweet tooth
• 'Sesame Street' figure
• Muppet with a voracious appetite
• 'Sesame Street' character
• Voracious Muppet
• Muppet appropriate for this puzzle
• Puppet who - [gasp!] - went on a diet in 2005