In a mixing bowl, add ¼ cup flour and ½ teaspoon of salt. Add chicken pieces and toss to coat.
Heat the oil in a large heavy pot on medium high heat, when hot, add the chicken in batches, cook about 10 minutes, turning the pieces as needed to to brown them on all sides. Remove chicken to a large plate and keep warm.
To the pot, add the onion, carrot, celery, garlic, bay leaf, and thyme. Cook 4-5 minutes or until the vegetables start to soften, turn them occasionally.
Add the broth, chicken, and ½ teaspoon of salt, bring to a boil, Reduce heat to medium low, cover and simmer for 30 minutes.
While the chicken is simmering, to a large mixing bowl add the remaining 1½ cups of flour, baking powder, sugar, and remaining ½ teaspoon of salt. Whisk to mix together.
To the flour mixture, stir in the parsley and beer until mixture is just moistened. Spoon 10-12 dumplings onto the chicken mixture.
Cook 9-10 minutes or until a toothpick inserted into the centers comes out clean.
Remove and discard the bay leaf. Serve the chicken and dumplings, enjoy.