In a shallow bowl, mix 1/2 cup flour, salt and pepper. Add chicken, 1 piece at a time, and toss to coat; shake off excess. In a 6-qt. stockpot, heat oil over medium-high heat. Brown chicken in batches on all sides; remove from pan.
Add onion, carrots and celery to same pan; cook and stir 6-8 minutes or until onion is tender. Add garlic; cook and stir 1 minute longer. Stir in 1/4 cup flour until blended. Gradually add stock, stirring constantly. Stir in wine, sugar, bay leaves and peppercorns. Return chicken to pan; bring to a boil. Reduce heat; simmer, covered, 20-25 minutes or until chicken juices run clear.
For dumplings, in a bowl, whisk flour, baking powder and salt. In another bowl, whisk milk and melted butter until blended. Add to flour mixture; stir just until moistened (do not overmix). Drop by rounded tablespoonfuls onto a parchment-lined baking sheet; set aside.
Remove chicken from stockpot; cool slightly. Discard bay leaves and skim fat from soup. Remove skin and bones from chicken and discard. Using 2 forks, coarsely shred meat into 1- to 1-1/2-in. pieces; return to soup. Cook, covered, on high until mixture reaches a simmer.
Drop dumplings on top of simmering soup, a few at a time. Reduce heat to low; cook, covered, 15-18 minutes or until a toothpick inserted in center of dumplings comes out clean (do not lift cover while simmering). Gently stir in cream, parsley and thyme. Season with additional salt and pepper to taste.