Stir half-and-half, chicken stock, diced tomatoes, tomato paste, and Worcestershire sauce together in a saucepan over medium heat; bring to a simmer and add sugar, garlic powder, onion powder, white pepper, and salt. Stir the mixture and continue to cook until hot, about 5 minutes.
Blend mixture with an immersion blender until smooth. Reduce heat to low and continue cooking until the mixture thickens, about 20 minutes.
