Place chicken carcass (and any leftover skin, meat and other bones) in a large pot and cover with cold water. Add bay leaf, and bring to a boil. Reduce heat, and simmer 60 to 90 minutes. Remove from heat, cool slightly, and strain. Remove chicken meat from carcass, and chop into bite-size pieces. Strain the stock.
In a large saucepan over medium heat, melt butter. Cook onion and shallots in butter until translucent. Pour in strained stock and chicken meat and stir in stock cubes, parsley, salt, pepper, potatoes and corn. Simmer 15 minutes, until potatoes are cooked and corn is tender. Remove from heat and stir in cream.