Cut corn kernels off cobs into a big bowl with a small bowl set upside down inside it. Place cobs into a large saucepan with a lid. Add broth and bring to a boil. Reduce heat to medium, cover, and cook 30 minutes. Drain.

Meanwhile, heat oil in a large pot over medium heat. Add onion and cook, stirring occasionally, about 8 minutes. Season with poultry seasoning, salt, and pepper. Add carrots and cook, stirring frequently, 5 more minutes. Add broth. Stir in sweet potatoes, potatoes, corn kernels, sugar, and bouillon. Bring soup to a boil, reduce heat to medium, and simmer about 20 minutes.

Stir rotisserie chicken into soup and simmer 5 minutes more.