In a slow cooker, heat the olive oil on the sauté setting (if available). Add the diced onion and minced garlic, cooking until fragrant and lightly golden, about 5 minutes.
Add the sliced carrots and celery to the slow cooker, stirring them into the onion and garlic mixture. Cook for another 3-4 minutes.
Layer the chicken breasts on top of the vegetables. Pour the chicken broth over the chicken, and season with dried thyme, paprika, salt, and pepper.
Cover the slow cooker and cook on low for 6-7 hours or on high for 3-4 hours, until the chicken is cooked through and tender.
Once cooking is complete, carefully remove the chicken breasts and shred them with two forks. Return the shredded chicken back to the slow cooker.
Stir in the cubed cream cheese until it melts and creates a creamy consistency. Mix until well combined.
Add the fresh spinach to the soup and stir until wilted, about 2-3 minutes. Adjust seasoning if necessary.
Serve the soup hot, garnished with a sprinkle of fresh herbs if desired.