Dice the chicken breasts into 1-inch pieces and chop the onions and carrots into small, even pieces. Prepare your skillet by heating a splash of oil over medium heat.
Sauté the onions in the skillet until translucent and fragrant, about 5 minutes. Add the diced carrots and cook for another 3 minutes until slightly softened and aromatic.
Transfer the sautéed vegetables to the slow cooker. Add the chicken pieces, pour in the chicken broth, and add the bay leaf and thyme. Stir gently to combine everything evenly.
Cover the slow cooker and cook on low for 4 to 6 hours, or until the chicken is tender and easily shredded, and vegetables are soft.
About 30 minutes before serving, remove the bay leaf. In a small bowl, whisk the flour or cornstarch with a little cold water to make a slurry, then stir it into the soup to help thicken. Add the softened cream cheese in chunks, stirring gently until fully melted and the soup is creamy and smooth.
Adjust the seasoning with salt and pepper, then let the soup sit off the heat for a few minutes to settle. Garnish with chopped fresh parsley for a burst of color and flavor.
Serve the soup hot in bowls, enjoying the thick, creamy texture and fragrant aroma that signals comfort in every spoonful.
