Heat olive oil in a large pot over medium heat. Add diced onion and cook for 5 minutes until softened and translucent.
Add minced garlic and cook for another minute until fragrant, stirring constantly to prevent burning.
Stir in crushed tomatoes, vegetable broth, tomato paste, basil, salt, and pepper. Bring to a boil, then reduce heat and simmer for 15 minutes.
Using an immersion blender, carefully blend the soup until smooth. Alternatively, transfer to a regular blender in batches (be careful with hot liquids!).
Remove from heat and let cool for 2-3 minutes. Whisk in Greek yogurt until fully incorporated and creamy.
Ladle into bowls and garnish with fresh basil if desired. Serve immediately with whole grain crackers or a small grilled cheese sandwich.