If using cooked chicken, shred or dice it into bite-sized pieces and set aside. If using raw chicken, pat the chicken breasts dry with paper towels and season both sides with salt and black pepper.
Heat 1 tablespoon of olive oil in a large soup pot over medium-high heat. Add the chicken breasts and sear for about 3–4 minutes per side until golden brown. Remove the chicken from the pot and set aside. If you're using cooked chicken, you can skip this step.
Reduce the heat to medium. Add the diced onion, carrots, celery, and minced garlic to the same pot. Cook for 5–8 minutes, stirring occasionally, until the vegetables start to soften.
Add the diced potatoes and 3 cups of chicken broth. If using raw chicken, slice the seared chicken breasts in half and return them to 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 you used raw chicken, carefully remove it from the pot and place it on a cutting board. Let it cool slightly before shredding or cutting it into bite-sized pieces. If you used cooked chicken, move on to the next step.
In a separate medium saucepan, melt the butter over medium heat. Whisk in the flour and keep stirring for 1–2 minutes until a smooth, lightly golden paste forms.
Slowly pour the milk into the butter and flour mixture, whisking constantly to prevent lumps. Add the heavy cream and continue cooking for about 5 minutes, until the sauce becomes thick and smooth.
Pour the creamy sauce into the soup pot. Add the shredded chicken and stir everything together until well combined. Stir in the corn and peas, if using, and let the soup simmer for another 2–3 minutes until everything is heated through.
If the soup is thicker than you like, slowly add the remaining chicken broth until it reaches your preferred consistency. Season with salt and black pepper to taste. Ladle into bowls and serve warm with biscuits, crackers, or crusty bread.