Sprinkle chicken with thyme, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Cook in 2 tablespoons hot oil in a Dutch oven over medium-high heat 8 minutes, turning to brown all sides. Stir in broth and wine; bring to a boil. Cover, reduce heat, and simmer 15 minutes. Drain chicken, reserving broth mixture. Wipe drippings from pan with a paper towel. Saute onions in 1 tablespoon hot oil in a skillet over medium-high heat 5 minutes. Add garlic; saute 1 minute.
Melt margarine in Dutch oven over low heat; add 1/4 cup flour, stirring until smooth. Cook 1 minute, stirring constantly. Add reserved broth mixture; cook over medium heat, stirring constantly, until mixture is slightly thickened and bubbly. Stir in whipping cream. Add chicken and onion mixture to broth mixture; bring to a boil.
Combine 1 1/3 cups flour, baking powder, and remaining 1/2 teaspoon salt and 1/4 teaspoon pepper; cut in shortening with a pastry blender until mixture is crumbly. Add milk; stir with a fork until dry ingredients are moistened. Drop batter by large spoonfuls into boiling broth mixture; cover, reduce heat to medium-low, and simmer 20 minutes or until dumplings are done.