Heat 3 to 4 tablespoons of olive oil in a large pot over medium heat. Add diced Vidalia onion, carrots, and celery. Cook, stirring occasionally, until onions are translucent and vegetables soften, about 6 to 8 minutes. Add sliced cremini mushrooms and cook until they release moisture and begin to brown, about 5 more minutes. Stir in minced garlic and cook for 1 minute until fragrant.
Sprinkle all-purpose flour over the sautéed vegetables. Stir continuously to coat the veggies and cook off raw flour taste, about 2 minutes, creating the creamy base for the soup.
Stir in kosher salt (start with 1 teaspoon), poultry seasoning, thyme, rosemary, and black pepper. Add rinsed wild rice and stir to combine, toasting the rice slightly in the pot.
Slowly whisk in the vegetable broth, dissolving any flour lumps. Add bay leaves and bring to a gentle boil. Reduce heat to low, cover, and simmer for 45 minutes to 1 hour until wild rice is tender and broth mostly absorbed.
Remove bay leaves. Stir in half-and-half or heavy cream and finely minced parsley. Add lemon juice and a pinch of sugar if using, to brighten and balance flavor. Taste and adjust salt and pepper as needed.
Ladle soup into bowls and garnish with extra parsley if desired. Serve with crusty bread or a simple green salad for a complete meal.
