Season the chicken breasts generously with salt and pepper. In a large pot, heat 2 tablespoons of olive oil over medium-high heat. Once the oil is shimmering, carefully add the chicken and sear for about 3-4 minutes on each side until golden brown. Remove the chicken from the pot and place it on a plate to rest.

In the same pot, add diced onion, chopped celery, and sliced carrots. Sauté these for 5-8 minutes until they become tender. Add minced garlic and cook for an additional minute.

Pour in about 1/2 cup of dry white wine, scraping the bottom of the pot to lift any browned bits. Simmer for 2-3 minutes to let the alcohol evaporate.

Add diced russet potatoes and 4 cups of low-sodium chicken broth. Bring to a simmer and return the seared chicken, submerging in the broth. Cook for 15-20 minutes until the potatoes are tender.

In a separate saucepan, melt 4 tablespoons of butter over medium heat. Whisk in 1/4 cup of all-purpose flour until golden, then gradually whisk in 1 cup of milk and 1 cup of heavy cream until thickened, about 5 minutes.

Remove the chicken, shred it, and return it to the pot along with the roux, 1 cup of frozen corn, and 1 cup of frozen peas. Stir to combine and heat through for an additional 2-3 minutes.

Taste and adjust seasoning with salt and pepper. Ladle into bowls and serve hot.