In a large Dutch Oven, over medium heat, heat the olive oil. Add the onion and sauté for a couple of minutes, until translucent. Then, add the carrots and celery, sautéing until softened, about 5 minutes. Finally, add the minced garlic and sauté until fragrant, about 1 minute.
Optional: pour in the white wine to deglaze the pot, scraping all the browned bits from the bottom.
Add the chicken breasts, chicken broth and bay leaves. Season with salt and pepper. Bring to a boil, then cover and lower to a simmer. Cook for 15 to 20 minutes, or until the chicken is tender.
While the chicken is cooking, cook the rice in a saucepan, according to package instructions. Reserve.
In another saucepan, melt the butter over medium heat. Add flour all at once and whisk vigorously. Cook until it starts to bubble and it turns slightly golden. Slowly add the milk, whisking constantly, until thickened. Add the heavy cream and remove from heat. Season with salt and pepper, and reserve.
When the chicken breasts are done cooking, remove to a cutting board and shred them. Reserve.
Add the white sauce to the soup broth. Raise the heat to medium high and bring to a boil, cooking until thickened to the desired consistency. Add the shredded chicken, cooked rice and chopped parsley.
Taste for seasoning and adjust salt and pepper.
Serve immediately!