Preheat oven to 400 degrees. Place halved tomatoes, onions, garlic, and thyme onto greased baking sheet and drizzle with olive oil. Generously season with salt and pepper. Roast in the oven for 30-40 minutes.
Once done roasting, allow ingredients to cool for at least 10 minutes. Remove leaves from thyme sprigs. Then add roasted ingredients to blender or food processor and blend until smooth.
Add milk, basil, Parmesan, tomato sauce, and sugar; continue to blend. Save one tablespoon of basil for garnish, if desired.
Transfer blended liquid to pot, add in oregano, and simmer on medium low for about 10 minutes.
Garnish with fresh basil, if desired.