Preheat your oven to 400°F (200°C).
In a baking dish, combine the cherry tomatoes and feta cheese. Drizzle with 2 tablespoons of olive oil, and sprinkle with salt, pepper, and half the dried oregano.
Roast in the oven for about 25 minutes or until the tomatoes are blistered and the feta is golden.
In a medium pot, heat the remaining tablespoon of olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until softened.
Stir in the minced garlic and cook for an additional minute until fragrant.
Once the tomatoes and feta are done roasting, carefully transfer them to the pot (scraping in all juices) and add the vegetable broth, remaining oregano, and red pepper flakes if using.
Bring the mixture to a simmer and cook for about 5 minutes to let the flavors meld together.
Using a blender (or an immersion blender), blend the soup until smooth and creamy. Adjust the seasoning with salt and pepper to taste.
Serve hot, garnished with fresh basil leaves, alongside crusty bread if desired.