Heat oil in large pot. Add onion and garlic - cook for 4 minutes. Remove with slotted spoon to small bowl.
Place chicken in pot in single layer. Cook over medium high heat for 5 minutes on each side or until lightly browned. Add onion and garlic mixture, carrots, parsnips, thyme, and salt to pot. Pour beer over chicken and vegetables.
Bring to a boil over high heat. Reduce heat to low. Cover and simmer for 40 minutes.
Add mushrooms and peas to skillet. Cover and cook for 10 minutes.
Uncover pot and increase heat to medium. Cook for 10 more minutes or until chicken is no longer pink in center.
Option 1 - serve chicken as is with vegetables. Or Option 2 - remove chicken from bones and cut into small pieces and serve with vegetables and Parmesan Chive biscuits.
Garnish dish with fresh parsley.