In a small saucepan over low heat, combine the chicken broth, bay leaf, and dried thyme. Bring just to a bare simmer and let infuse for 10 minutes; keep warm on the lowest heat.
Make the dumpling dough: In a medium bowl whisk together the flour, baking powder, and salt. Cut in the cold butter with a pastry cutter or fingertips until the mixture looks like coarse crumbs. Add the cold milk and stir just until no dry pockets remain. Cover and refrigerate while you start the soup base.
Melt the butter in a Dutch oven over medium heat. Add onion, carrots, celery, dried parsley, salt, and pepper. Cook, stirring occasionally, until the vegetables are glossy and lightly golden at the edges, 8–10 minutes. Stir in the garlic and cook 30 seconds.
Sprinkle the flour over the vegetables and cook, stirring constantly, for 2 minutes to form a blond paste.
While stirring, slowly stream in the warm infused broth (including the bay leaf and thyme). Bring to a gentle simmer and cook until slightly thickened and the flavors meld, about 8 minutes on medium-low heat.
Stir in the shredded chicken and return to a gentle simmer for 3 minutes to warm through. Taste and adjust seasoning.
Reduce the heat to low so the surface barely simmers. Using two spoons, drop heaping tablespoonfuls of chilled dumpling dough onto the surface of the soup, spacing them slightly. Cover the pot and steam the dumplings without lifting the lid for 6–8 minutes, until puffed and cooked through.
Turn off the heat. Discard the bay leaf, then stir in the heavy cream and lemon juice. Let the soup rest 3 minutes so the dumplings set, then ladle into bowls and serve.