In a large pot over medium heat, add oil. Once hot, add onion and garlic. Cook until tender, approximately 5 minutes.
Stir in ginger, crushed red pepper flakes, and curry powder. Fry for 30 seconds or so.
Add diced tomatoes and vegetable broth. Stir in fresh basil, sugar, salt, and pepper. Bring to a simmer and let cook for 15 minutes.
Use a hand immersion blender or a regular blender, blend the soup until smooth. Stir in Greek yogurt.
Add in cheese tortellini and cook on medium-low heat until the pasta is cooked through, approximately 7 to 8 minutes.
Serve warm with crusty bread on the side.