Heat a 12-inch non-stick skillet over medium heat, add walnuts and gently toast in dry pan, stirring frequently, for 5 or so minutes; do not allow them to scorch. Remove walnuts from pan and set aside.
Add oil and butter to hot skillet, and when melted, add ginger, carrots and red pepper flakes and saute over medium heat for 2 or so minutes, stirring frequently. Add garlic and saute for another 30-60 seconds, taking care not to burn the garlic. Add chicken stock, soy sauce, sugar and chard and cook, uncovered, for about 8-10 minutes, stirring and turning several times so it cooks evenly. Broth will condense and evaporate during cooking time. (Add 1-2 tablespoons of water to the pan if the liquid dries up before the chard is tender enough.) When chard is cooked, add walnuts and cook and stir to heat through, 1 more minute.