Prepare 4 frozen buttermilk biscuits according to package directions.
Meanwhile, in a large mason jar, shake together chicken stock, whole milk, flour, and poultry seasoning. Cook onion and carrots in butter in a large saucepan over medium-high heat until softened, 2 to 3 minutes. Slowly whisk in milk mixture. Bring to a boil, reduce heat, and simmer, stirring often, until thickened, 6 to 8 minutes.
Stir in shredded rotisserie chicken, green beans, and flat-leaf parsley and cook until warm, 4 to 5 minutes. Season with kosher salt and black pepper. Serve topped with biscuits.