Rustic Tofu and Vegetable Wild Rice Soup

Name: Rustic Tofu and Vegetable Wild Rice Soup
Ingredients: 2 Tablespoons olive oil; 1 Cup diced onion; 3/4 Cups diced celery; 1 Cup sliced carrots; 3/4 Cups chopped mushrooms; 3/4 Teaspoons kosher salt; 1 Teaspoon oregano; 1/2 Teaspoon ground black pepper; 3/4 Cups dry wild rice; 5 Cups low-sodium vegetable broth; 2 Sprigs fresh thyme; 1 Tablespoon cornstarch; 1 Cup half and half; 2 1/2 Tablespoons Dijon mustard; 1 Package tofu, such as House Foods firm organic tofu, pressed and cut into 1/2 inch cubes; 1/4 Cup fresh minced parsley