Combine 2 pounds chicken thighs, 2 teaspoons kosher salt and 4 cups water in a medium saucepan. Bring to a boil, then reduce heat to medium-low and simmer, partially covered, until chicken is cooked, about 20 minutes. Transfer chicken to a plate; let cool 10 minutes. Discard skin and bones; shred meat into bite-size pieces (you should have 3 cups). Strain broth (you should have 4 cups; if not add more water).

Melt 4 tablespoons butter in a large pot over medium-high heat. Add 1 diced onion; 3 diced carrots; 1 diced celery stalk; 8 ounces potatoes, peeled and cut into a 1/2-inch dice; and 1 1/4 teaspoons thyme. Cook, stirring, until onion is translucent, 3 to 4 minutes. Sprinkle with 1/4 cup flour; cook 30 seconds. Gradually stir in a broth. Bring to a boil, then reduce heat to medium and simmer 2 minutes. Stir in chicken, 1 cup partially defrosted peas, and 3 tablespoons chopped parsley.

Season with salt and freshly ground pepper.

Meanwhile, whisk together 1 3/4 cups flour, 1 1/2 teaspoons salt, 3/4 teaspoons pepper 2 teaspoons baking powder and 3 tablespoons chopped parsley. Cut into 4 tablespoons cold butter. Stir in 3/4 cup milk until dough holds together. Drop 8 heaping spoonfuls of dough on top of chicken mixture. Cover and simmer until dumplings are cooked through, about 12 minutes. Serve with more chopped parsley and lemon wedges.