Add chicken broth to pot and stir to combine. Immediately add cornmeal to pot in a steady stream stirring constantly to avoid forming lumps. Bring to a low simmer. Turn heat to very low, cover saucepan and cook approximately 10 minutes until cornmeal is soft and texture is no longer gritty.
Season to taste with lime juice, salt and pepper.
For Vegan version
Omit meat but use all other marinade ingredients. Substitute vegetable broth for chicken broth.
Combine all ingredients in pot and bring to a low boil over medium heat. Continue with steps 5 and 6 as above. If desired for texture, add seasoned sautéed onions and mushrooms to mixture just before serving.