Place the peppers on a cutting board, and cut about 1/8-inch off their bottoms so they will stand upright.
Cut the tops of each pepper about half an inch or a bit more. From the tops, remove all the flesh and discard the stems.
Take out the seeds and as much membrane as you can. Combine the peppers with a cup of water in a microwave-safe bowl.
Place the plastic wrap in the microwave and heat the unit for about ten minutes on high power. Cover and let them sit until ready to stuff.
In a large frying pan over medium-high heat, heat 2 tablespoons of olive oil.
Ensure the beef is evenly distributed and cook undisturbed until lightly browned approximately 3 to 5 minutes.
Stir and fry until the meat is lightly browned all over, breaking up any clumps with a spoon and scraping up any browned bits from the pan. Transfer the beef to a large bowl after it has been cooked well.
Reduce the heat to medium and add the reserved chopped peppers, onions, garlic, thyme, 4 teaspoons salt, and 1/2 teaspoon pepper to the same frying pan.
Cook for about 10 to 12 minutes, stirring occasionally, until tender but not browned. It takes about 10 minutes to cook the tomatoes until they fall apart and most of the liquid has evaporated.
Add the tomato paste and stir constantly until brick red, about two minutes. Add the vinegar and cook until the mixture is reduced, very thick, and if using wine so until no alcohol smell remains.
Add the broth to the bowl with the beef and bring to a boil. Stir in the rice until it is completely combined. Add salt and pepper to taste.
Prepare the oven by preheating it to 450 degrees Fahrenheit. Using the back of a spoon, gently press the filling into the peppers, cut side up, in a baking pan.
Don't overfill the peppers and split their sides. Bake for 15 minutes, then top with cheese and bake for 10 to 12 minutes more until the cheese is melted and browned in spots. With a side dish of your choice, serve it hot. Enjoy!