On a cast-iron pan, turn on medium heat, add the following ingredients successively: onion, olive oil, 1/2 tablespoon of garlic powder, ground black pepper, brown gravy mix, salt, mustard, 1/2 teaspoon of Worcestershire sauce, ketchup, tomato sauce, and chicken broth.
Remove the sauce from the pan, set aside.
Cook the vegetables & beef:
On the same pan, turn on medium heat, add successively: green bell pepper, yellow bell pepper, carrot, butter. Stir them around for 3 minutes until tender.
Continue to add ground beef, 1/2 tablespoon of garlic powder, and 1/2 teaspoon of Worcestershire sauce.
Pour the sauce back to the pan, let simmer for 10 minutes.
Sprinkle cheddar cheese on top, stir for a minute one last time. Remove the pan from heat.
Slice the hamburger buns in half, toast them in the oven at 350°F for 5 minutes.
Spread the sloppy beef on the toasted buns and serve immediately.
If you want to make it more beautiful, serve each bun on a dish with a crispy and fresh lettuce leaf.