Heat butter and olive oil in a large pot over medium-high heat. Add in cauliflower, onions, celery, and carrots. Cook for 10 to 12 minutes, stirring occasionally, until vegetables begin to soften.
Add the garlic and saute 1 minute more. Stir in thyme, oregano, and cornstarch and cook for 1 minute.
Pour in the vegetable broth and milk. Stir constantly until the mixture comes to a boil.
Reduce the heat to low and simmer 3 to 5 minutes until the soup has thickened. Season with salt and pepper to taste. Serve hot.