Heat 1 tablespoon olive oil in a large pot or Dutch oven over medium-high heat.
Add 1 finely diced white onion and sauté until softened and translucent.
Add 2 lbs stew meat cut into 1-inch pieces and brown the beef for approximately 5–6 minutes, breaking it apart with a wooden spoon as it cooks.
Stir in 1 tablespoon minced garlic and cook for 1 minute until fragrant.
Add 2 tablespoons chili powder, 1 teaspoon cumin, 1 tablespoon smoked paprika, 1 tablespoon Italian seasoning, 1 tablespoon brown sugar, ½ teaspoon black pepper, and 1 teaspoon salt. Stir until the beef is evenly coated with the seasonings.
Stir in 1 can (15 oz) crushed tomatoes, 1 can (15 oz) drained and rinsed red kidney beans, and 1 tablespoon white vinegar.
Bring the chili to a simmer and cook for approximately 15 minutes, stirring every 5–7 minutes.
Stir in 2 tablespoons cornmeal and reduce the heat to low. Cook for an additional 10–15 minutes until the chili thickens.
Remove the chili from the heat and let it rest for 5 minutes.
Serve warm topped with 1 cup cheddar cheese and 2 sliced green onions.