Prepare the chicken. Lightly flatten the chicken breasts to an even thickness. Season both sides with salt and black pepper.
Sear the chicken. Heat a little cooking oil in a large pot over medium-high heat. Sear the chicken on both sides until golden brown, but do not cook it completely through. Remove it from the pot, cut it into bite-sized pieces, and set aside.
Cook the vegetables. Add the diced onion and minced celery to the same pot. Cook until softened, scraping up the browned bits left from searing the chicken. Reduce the heat to medium.
Make the roux. Add the butter and allow it to melt. Stir in the flour and cook for approximately 2 minutes, stirring continuously to remove the raw flour taste.
Make the creamy sauce. Gradually whisk in the chicken broth first to take the majority of the heat, followed by the milk, until the flour is fully incorporated and the sauce is smooth.
Add the seasonings and vegetables. Crumble in the chicken bouillon cube, then stir in the garlic powder, celery seed, and frozen mixed vegetables.
Finish cooking the chicken. Return the partially cooked chicken pieces and any accumulated juices to the pot. Reduce the heat to low, cover, and maintain a gentle simmer for approximately 15–20 minutes. Stir every 5 minutes to prevent sticking. Continue cooking until the chicken reaches an internal temperature of 165°F.
Taste and serve. Taste the filling and adjust the salt and black pepper as needed. Allow it to cool slightly before serving.