Heat the vegetable oil in a large pot or Dutch oven over medium heat.
Add the chopped onion and cook until softened, about 5 minutes.
Stir in the minced garlic and cook for another minute.
Add the beef or chicken cubes and cook until browned on all sides.
Stir in the diced tomato and cook for a few minutes until it starts to break down.
Pour in the beef or chicken broth and bring to a boil.
Reduce heat to low and simmer for about 30 minutes.
In a bowl, mix the cornmeal with 1 cup of water to form a thick batter. You can add grated cheese to the batter if desired.
Season the batter with salt, black pepper, and dried oregano.
Add the sliced carrots and cubed potatoes to the pot with the meat and broth.
Drop spoonfuls of the cornmeal batter into the simmering stew. The batter will cook and form dumplings.
Cover the pot and cook for an additional 20-25 minutes, or until the dumplings are cooked through and the vegetables are tender.
Stir in the chopped fresh cilantro or parsley.
Enjoy your meal!