Heat a large pot over medium heat, add the olive oil and heat through. Add the onion and sauté, stirring occasionally, until the onion is translucent, about 6 minutes. Add the garlic and continue to cook until the garlic is fragrant, about 1 minute.
Stir in the tomato paste then add the tomatoes with their liquid, chicken broth, thyme, sugar, salt, pepper and paprika. Bring the mixture to a boil, then reduce the heat to medium-low and simmer for 45 minutes.
Remove the pot from the heat and let cool. Discard the thyme then once cool to the touch, use a blender to puree the soup in batches until all of the soup is well blended.
Return the mixture to the pot and slowly whisk in the cream and the Cheddar cheese. Continue to whisk until the cheese has completely melted and is thoroughly combined.