Melt the butter in a large pot over medium heat. Add the chopped sweet onion and sauté until translucent and fragrant, about 5 minutes.
Sprinkle in the all-purpose flour while stirring continuously. Cook for about 2 minutes to create a roux.
Gradually whisk in the chicken stock, ensuring no lumps from the roux. Add the canned diced tomatoes, sugar, salt, and pepper. Bring to a simmer and cook for about 20 minutes.
Prepare the cheddar bay dumplings according to package instructions by combining them with melted butter.
Drop spoonfuls of dumpling batter onto the surface of the simmering soup. Cover and let them steam on low heat for about 10 minutes.
Ladle the tomato soup into bowls and top with the cheddar bay dumplings. Serve warm.