Heat olive oil in a large pot over medium heat. Sauté onion, carrots, and celery until soft, about 5 minutes. Season with salt, black pepper, and crushed red pepper.
Add garlic, basil, thyme, and roasted red peppers; cook 1-2 minutes until fragrant.
Stir in crushed tomatoes and vegetable broth; bring to boil, then reduce heat and simmer 30 minutes.
Using an immersion blender, puree soup until completely smooth.
Stir in Greek yogurt and serve immediately, garnished with fresh basil leaves.