Prepare the Vegetables: In a big pot, warm up the olive oil over medium heat. Add the celery, sliced carrots, and chopped onion. Sauté the veggies till they get tender, about 5-7 minutes. Add minced garlic and cook for another minute until fragrant.
Thicken the Soup: Sprinkle the flour over the sautéed vegetables, stirring continuously until the raw flour disappears.
Add Liquids: Gradually pour in the chicken broth, whisking constantly to ensure a smooth mixture without lumps.
Add Rice and Season: Stir in the Italian seasoning and uncooked jasmine rice. Bring to a boil, then reduce heat to low and simmer uncovered, allowing the rice to cook and absorb flavors.
Cook the Chicken: In a separate pan, cook the chicken pieces in a bit of olive oil until fully cooked. Then, add the cooked chicken to the soup pot.
Cream it up: Pour the heavy or whipping cream into the pot, stirring well to combine. Season with salt and pepper to taste.
Final Simmer: Allow the soup to simmer for a few more minutes on low heat for flavors to meld. Serve hot, garnishing with fresh herbs if desired.