Heat olive oil in a large stockpot over medium heat.
Once hot, add in onions, celery, carrots, and garlic and spices. Cook for 5-10 minutes, or until onions have softened.
Stir in cornstarch and cook for 60 seconds.
Stir in chicken broth, milk, potatoes, turkey, green peas, and black eyed peas.
Bring to a simmer, cover, and simmer for 15 minutes, or until potatoes are tender. Stir occasionally.
Taste and re-season, if necessary, and enjoy!