Dice onion; cut carrots and celery into 1/2-inch pieces; mince garlic.
Add vegetables, garlic, herbs, 1/2 teaspoon salt, pepper, 2 cups broth and bay leaf to a 6-quart slow cooker. Arrange thawed chicken over vegetables and season with remaining salt.
Cover and cook on low 4 1/2 to 5 1/2 hours or high 2 1/2 to 3 1/2 hours, beginning checks at the earliest time.
Remove each thigh when its thickest center reaches 165°F. Rest 5 minutes, discard bay leaf and shred chicken into bite-size pieces.
Whisk flour with reserved 1 cup cool broth. Boil with 2 cups cooking liquid in a saucepan for 2 to 3 minutes, then return thickened sauce to cooker.
Bake biscuits separately on a sheet pan according to package directions until deeply golden and fully baked in the center. Cool briefly on a rack.
Add shredded chicken, peas and corn; cover on high 5 to 10 minutes. Switch off cooker and stir in cream, lemon juice and parsley; adjust seasoning.
Ladle hot filling into bowls and top each portion with a split warm biscuit immediately before serving.