In a large pot over medium heat, melt 2 tablespoons of butter and add 1 diced onion. Sauté until translucent, about 5 minutes. Sprinkle in 2 tablespoons of flour, stirring for 1 minute to make a roux. Gradually add 4 cups of chicken broth and 2 cans of diced tomatoes, stirring until smooth. Bring to a boil, then reduce heat to a simmer. Season with 1 teaspoon of sugar, salt, and black pepper to taste.

For a velvety texture, blend the soup in batches until smooth. Return the blended mixture to the pot over low heat. Allow to simmer for an additional 5-10 minutes.

In a mixing bowl, prepare the dumplings by combining 2 cups of Bisquick with 1 cup of shredded cheddar cheese and 2/3 cup of milk. Stir until just combined.

Drop spoonfuls of dumpling batter into the simmering soup. Cover the pot and let the dumplings steam for 15-20 minutes until fluffy.

Melt 2 tablespoons of additional butter and mix with the seasoning packet. Brush this mixture over the dumplings before serving. Ladle the rich tomato soup into bowls and serve hot.