Grillades and Grits a classic New Orleans brunch

Name: Grillades and Grits, a classic New Orleans brunch
Ingredients: 2 pounds beef top round, ¼ thick; 1 cup all purpose flour; salt and black pepper to taste; 5 Tablespoons vegetable oil, plus more if necessary; 1 large onion, diced; 1 green bell pepper, diced; 3 stalks celery, diced; 1 jalapeno pepper, seeded and minced; 3 cloves garlic, minced; 1 teaspoon dried oregano; 1 teaspoon dried thyme; 1 teaspoon dried basil; 1½ teaspoons Creole seasoning (such as Tony Cachere's); 2 cups beef stock; 14 oz. crushed tomatoes or tomato puree; 2 bay leaves; dash of Worcestershire sauce, to taste; pinch of cayenne pepper, to taste; sliced green onion tops, for garnish; 1 cup old-fashioned grits; 5 cups milk (any kind); salt and pepper to taste; 1½ cups grated cheese (cheddar, pepper jack, goat, or a combination); Tabasco sauce, to taste