Heat 2 tablespoons butter and 1 tablespoon olive oil in a dutch over medium heat. Add 1/2 cup diced onion, 1/2 cup sliced celery, and 1 cup chopped carrot. Cook for 3–4 minutes until the onion softens, stirring occasionally.
Stir in 1 tablespoon minced garlic, 1 cup chopped green beans, 1 cup sliced mushrooms, 1 cup frozen broccoli florets, and 1 cup frozen corn kernels. Cook for 2–3 minutes. Mix in 1 teaspoon dried thyme, 1 teaspoon dried oregano, and 3 tablespoons all purpose flour, stirring constantly for 1–2 minutes to cook the flour.
Slowly pour in 4 cups whole milk and 2 cups vegetable broth, stirring continuously. Bring to a gentle boil, then reduce the heat to a simmer.
Season with salt and pepper, and let simmer for 6–7 minutes, stirring occasionally, until the soup thickens.