Preheat the oven to 400ºF.
Prepare a large baking sheet lined with parchment paper. Place the halved tomatoes and garlic cloves on the baking sheet, drizzle with 2 tablespoons of olive oil, and sprinkle it with oregano, salt, and black pepper.
Place the baking sheet in the oven and roast for 45 minutes or until the tomatoes are soft and juicy.
Remove the roasted garlic from the peels and roughly chop them. Set aside.
In a large stockpot, heat the remaining tablespoon of olive oil, over medium heat, and sauté onions until tender, about 3 to 5 minutes.
Add in roasted garlic, tomatoes, red pepper flakes, broth, basil, and thyme. Simmer on low for 30 minutes then remove from heat.
If you’re using a hot-liquid-friendly blender, you may pour the soup into the blender right away. Otherwise, cool down the mixture to room temperature before transferring it to the blender (see notes). Season with salt and pepper, to taste.
Transfer the soup into bowls and garnish with basil and Parmesan cheese, if desired. Serve warm.