Place the whole chicken in a large Dutch oven. Add 10 cups chicken stock—enough to mostly cover the chicken. Add thyme and bay leaves.

Bring to a gentle simmer over medium-low heat. Cover and cook 35–45 minutes, turning once or twice, until the chicken is fully cooked and very tender.

Remove the chicken to a plate. Skim excess fat from the broth, leaving some for flavor.

Let the broth simmer uncovered 5–10 minutes to concentrate slightly. You should have about 8 cups of broth remaining.

Discard skin and bones. Shred or chop the meat into bite-size pieces. Set aside.

Remove biscuits from cans. Working with one at a time, roll each biscuit into a rope about 6–8 inches long. Cut into ½–¾-inch pieces.

Bring the broth to a steady simmer (not a rolling boil).

Add biscuit pieces, stirring gently once or twice so they do not stick together.

Simmer uncovered 18–22 minutes, stirring occasionally, until dumplings are cooked through and the broth has thickened noticeably.

Reduce heat to low. Stir in butter until melted.

Slowly stir in milk. Do not boil after adding milk.

Season with kosher salt and black pepper, tasting as you go.

Return shredded chicken to the pot and simmer 5 minutes more to allow flavors to come together.

Remove bay leaves before serving.

Serve hot.