Season chicken breasts with salt and pepper. Heat 1 tbsp of olive oil in a large pot or Dutch oven over medium-high heat. Add chicken and sear on both sides until golden, about 3-4 minutes per side. The chicken does not need to be cooked through. Remove from the pot and set aside.

Add the remaining 1 tbsp of olive oil to the pot. Add the diced onion, carrots, and celery. Sauté for 5-7 minutes, stirring occasionally, until softened. Add the minced garlic and cook for another minute until fragrant.

Sprinkle the flour over the vegetables and stir continuously for 1 minute to cook out the raw flour taste. This roux will thicken the soup.

Gradually whisk in the chicken broth until smooth. Add the cubed potatoes, dried thyme, and the bay leaf. Return the seared chicken breasts to the pot.

Bring the soup to a boil, then reduce the heat to low, cover, and let it simmer for 15-20 minutes, or until the potatoes are fork-tender and the chicken is fully cooked (reaches an internal temperature of 165°F / 74°C).

Carefully remove the cooked chicken breasts and place them on a cutting board. Use two forks to shred the chicken, then return it to the pot. Remove and discard the bay leaf.

Stir in the heavy cream and chopped fresh parsley. Warm through gently for 2-3 minutes over low heat, but do not let the soup come back to a boil.

Season to taste with additional salt and pepper. Ladle the hot soup into bowls and garnish with crispy bacon, shredded cheddar, and chives, if desired.