In a large pot, heat 1 tablespoon of olive oil over medium-high heat. Season the chicken breasts with salt and pepper, then add them to the pot. Sear the chicken for about 3-4 minutes on each side until golden brown. Once cooked through, remove the chicken from the pot and set aside on a plate to rest before chopping.

In the same pot, reduce heat to medium and add the remaining tablespoon of olive oil. Sauté minced garlic, diced onions, chopped celery, and carrots for about 5-8 minutes until softened and fragrant.

Add the ¼ cup of dry white wine to the sautéed vegetables and stir well, scraping the fond off the bottom of the pot. Next, add the diced russet potato and 3 cups of chicken broth. Return the seared chicken to the pot, cover, and let it simmer for 15-20 minutes, or until the chicken is cooked through and the potatoes are fork-tender.

While the soup simmers, take a separate saucepan and melt 5 tablespoons of butter over medium heat. Once melted, whisk in ¼ cup plus 1 tablespoon of all-purpose flour to create a roux, cooking for about 5 minutes until it turns a light golden color.

Gradually whisk in 1½ cups of milk and ½ cup of heavy cream into the roux until it thickens to a gravy-like consistency. Keep whisking constantly to avoid lumps for about 3-4 minutes.

Once the chicken is cooked, remove it from the soup pot and chop it into bite-sized pieces. Stir the roux mixture into the soup, followed by the chopped chicken, and add frozen corn and peas if using them. Heat everything together for an additional 2-3 minutes.

If the soup is too thick, feel free to thin it out by adding more chicken broth. Taste and season with salt and black pepper as needed. Serve hot.