Heat 3 tablespoons salted butter and 1 tablespoon cooking oil in a large pot over medium-high heat. Add in the diced 1 white onion. Cook for 6 to 8 minutes, stirring occasionally, until onions begin to soften
Add the minced 1 tablespoon garlic and saute 1 minute more. Stir in 1 teaspoon dried thyme, 1 teaspoon dried oregano, and 1/4 cup all-purpose flour and cook for until flour has become more golden about 2 minutes.
Pour in the 4 cups vegetable broth, 2 cups milk. and 2 cups heavy cream. Stir constantly until the mixture comes to a boil. Add in 6 cups broccoli florets.
Reduce the heat to low and simmer 8-10 minutes until the soup has thickened and broccoli has softened. Add in shredded 2 cups cheddar cheese and stir. Season with salt and pepper to taste. Serve hot.