Pat the chicken breasts dry and season with salt and pepper. Heat a tablespoon of olive oil in a large pot over medium-high heat. Add the chicken and sauté for 3-4 minutes on each side until golden brown. Remove chicken and set aside.

In the same pot, add another tablespoon of olive oil if needed. Add garlic, onion, celery, and carrots. Sauté for 5-8 minutes until softened and onions are translucent.

Add diced potatoes and chicken broth to the pot, then return seared chicken. Bring to boil, then reduce heat and simmer for 15-20 minutes until chicken is cooked and potatoes are tender.

Prepare the roux in a separate pan by melting butter and whisking in flour for 2-3 minutes. Gradually stir in milk and heavy cream until thickened, about 5 minutes.

Add the roux to the soup, mix well. Chop cooked chicken into bite-sized pieces and combine back into the soup.

Stir in corn and peas, heat through for another 2-3 minutes. Adjust thickness with chicken broth as desired and season to taste.

Ladle soup into bowls and serve hot, possibly with crusty bread or salad.