Heat olive oil in a large pot over medium heat.
Add diced yellow onion and cook for 5 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add chopped yellow tomatoes and chopped carrot to the pot. Cook for 8 minutes, stirring occasionally.
Pour in vegetable broth and add salt, black pepper, ground turmeric, and dried thyme. Stir to combine.
Bring the mixture to a boil, then reduce heat to low and simmer uncovered for 20 minutes until vegetables are tender.
Remove the pot from heat and let cool slightly.
Using an immersion blender, blend the soup until smooth and creamy. Alternatively, carefully transfer the soup in batches to a blender and puree until smooth.
Return the blended soup to the pot and stir in the heavy cream and fresh lemon juice.
Heat the soup gently over low heat for 3-5 minutes without boiling, stirring occasionally.
Taste and adjust seasoning with additional salt or pepper if needed.
Ladle the creamy yellow tomato soup into bowls and garnish with chopped fresh chives before serving.