In a small bowl combine 1 cup very hot water and 1 teaspoon beef bouillon. Stir until bouillon has dissolved. Set aside.
In a large skillet, over medium heat, brown ground beef, breaking it up as it cooks.
Add diced onion, and green bell pepper.
Cook until beef is cooked through and onions and peppers are soft.
Drain off any excess fat.
Season with salt and steak seasoning.
Sprinkle cornstarch over the beef/onion/pepper mixture in the pan. Stir until beef is coated with the cornstarch.
Add reserved beef broth and the A-1 sauce to the skillet.
Stir together, increase heat and bring the mixture to a boil.
One mixture has come to a boil, reduce heat and allow mixture to simmer, stirring occasionally, for 5 minutes or until thickened.
Mixture will thicken even more once it's removed from heat.
While meat simmers on the stove, cut rolls or buns in half and place them, cut side up on a cookie sheet.
Lightly butter each cut side and place them cut side up in the oven.
Turn heat to broil and toast until lightly browned.
Remove from oven. Top toasted buns with sliced cheese.
Return to the oven and broil until the cheese is melted and gooey.
Pile meat filling onto each bun to serve.