Heat vegetable oil (2 tablespoons) in a large saucepan over high heat.
Add chicken thighs (3 pounds) *in batches* to brown both sides of the chicken.
Remove cooked chicken to a plate on the side, and continue cooking remaining pieces.
Add remaining oil to the saucepan and lower the heat to medium.
Once oil begins to shimmer, add chopped yellow onion (1 large), and celery ribs (2 sliced 1/4" thick) until soft, about 10 minutes.
Stir in minced garlic (1 tablespoon) and thyme (1/2 teaspoon) and cook until fragrant, about 2 minutes.
Add dry sherry (1/4 cup) and stir, loosening the brown bits at the bottom of your saucepan.
Add the chicken broth (6 cups), chicken flavor Better Than Bouillon (2 teaspoons), black pepper (1/2 teaspoon), carrots, bay leaves (2) and the browned chicken + accumulating juices on the plate.
Cook uncovered for 1 hour, or until the chicken is tender.
Meanwhile, cut your cauliflower (1 head) into dumpling sized florets.
Add them to your soup after it has cooked for 1 hour. Then, continue to cook the soup uncovered for 1 more hour.
Remove chicken from saucepan and place on a cutting board.
Once cooled, shred the chicken into bite sized pieces.
Remove bay leaves and any fat that is floating in the soup.
Add chicken back to the saucepan along with the chopped parsley (3 tablespoons), heavy whipping cream (1/2 cup) and cream cheese (4 Ounces).
Stir together to combine until cream cheese has melted.
Remove from heat and divvy into bowls. Top with fresh parsley and enjoy!