How to Make Chicken Stock Three tried and true methods for making GREAT homemade chicken stock. One method involves simmering a chicken carcass with vegetables. The other methods require sautéing chopped pieces of backs and wings first, before simmering with water and veggies. Matzo Ball Soup Homemade matzo ball soup for Passover or anytime! Light, clear broth. Fluffy matzo balls. Add chicken meat for a heartier meal.