Season chicken with salt and pepper. 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 for 6-8 minutes or until onion is tender. Add garlic; cook and stir 1 minute longer. Stir gluten-free flour until blended. Gradually add stock, stirring constantly. Stir in wine, sugar and bay leaves. Return chicken to pan; bring to a boil. Reduce heat; simmer, covered, for 20-25 minutes or until chicken is no longer pink.
For dumplings, in a bowl, whisk gluten-free flour, baking powder, sugar and salt. In another bowl, whisk buttermilk and butter until blended. Add to dry mixture; stir just until moistened (do not overmix). Drop dough 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. 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.