If using cooked chicken, shred or dice it into bite sized pieces and set it aside. If using raw chicken, pat the chicken breasts dry with paper towels and season both sides generously with salt and black pepper.
If using raw chicken, heat 1 tablespoon of olive oil in a large soup pot over medium to high heat. Add the chicken breasts and sear for approximately 3–4 minutes per side, until golden brown. Remove the chicken from the pot and set aside. If using cooked chicken, skip this step.
Reduce the heat to medium. Add the diced onion, carrots, celery, and minced garlic. Sauté for 5–8 minutes, stirring occasionally, until the vegetables begin to soften.
Add the diced potatoes and 3 cups of chicken broth. If using raw chicken, slice the seared chicken breasts in half and place them back into the pot. Bring everything to a gentle simmer and cook for 15–20 minutes, or until the potatoes are tender and the chicken reaches an internal temperature of 165°F.
If using raw chicken, carefully remove the cooked chicken and place it on a cutting board to cool slightly. If using cooked chicken, continue to the next step.
Melt the butter in a separate medium saucepan over medium heat. Whisk in the flour and continue stirring until a smooth, lightly golden paste forms, about 1–2 minutes.
Gradually pour the milk into the butter mixture, whisking constantly to prevent lumps. Add the heavy cream and continue cooking for approximately 5 minutes, until the mixture becomes thick, smooth, and creamy.
Pour the creamy mixture into the soup pot along with the shredded chicken and stir until completely combined with the broth and vegetables. Stir in the corn and peas, if using, and allow everything to simmer for another 2–3 minutes until heated through.
If the soup is thicker than desired, gradually stir in the remaining chicken broth until it reaches your preferred consistency. Season with salt and black pepper to taste. Ladle the soup into bowls and serve warm with biscuits, crackers, or your favorite crusty bread!