Dice the chicken into roughly 2-inch chunks and chop the carrots and onion into small, manageable pieces. Mince the garlic finely.
In a skillet over medium heat, sauté the diced onion and minced garlic until fragrant and translucent, about 3-4 minutes. This deepens their sweetness and aroma.
Transfer the sautéed onions and garlic to the slow cooker. Add the chicken chunks and chopped carrots on top.
Pour in the chicken broth, ensuring the ingredients are mostly submerged. Sprinkle dried thyme and parsley over the top, then season with salt and pepper to taste.
Cover the slow cooker and cook on low for about 6 hours, until the chicken is tender and the vegetables are soft. The house will fill with a warm aroma during this time.
About 30 minutes before serving, open the lid and stir in the chunks of cream cheese. Allow it to melt into the soup, creating a rich, velvety texture, stirring gently to help blend smoothly.
Pour in the milk or heavy cream, stirring well to incorporate. Turn the slow cooker to warm or low if needed, and let the soup thicken slightly for about 10 minutes.
Taste the soup and adjust seasoning with additional salt, pepper, or herbs if desired. The soup should be creamy, smooth, and fragrant.
Serve the soup hot in bowls, garnished with fresh parsley if preferred. Enjoy the comforting, velvety goodness in every spoonful.