Step 1

If your peppers don't sit upright on your cutting board, trim about 1/8-inch off the bottoms to even them out so they can stand without falling over. Cut the top off each pepper about 1/2-inch down. Remove and discard the stems, then finely chop the remaining flesh from the tops. Scoop out the seeds and as much of the membranes as you can. Place the peppers in a large microwave-safe bowl with 1/2 cup water. Cover with plastic wrap and microwave on high power for 12 minutes. Carefully uncover and let them sit until ready to assemble.

Step 2

Heat 2 tablespoons of the oil in a large skillet over medium-high heat. Spread the beef in an even layer and cook undisturbed until lightly browned, about 3 minutes. Toss and continue to cook, breaking up any clumps with the back of a spoon and scraping up any browned bits from the pan until the meat is lightly browned all over, 6 to 8 minutes. Transfer the browned meat to a large bowl with a slotted spoon.

Step 3

Reduce the heat to medium. Heat the remaining 1 tablespoon oil and add the reserved chopped peppers, onions, garlic, thyme, 4 teaspoons salt and 1/2 teaspoon pepper and cook, stirring occasionally, until tender but not browned, 10 to 12 minutes. Add the tomatoes and cook, stirring occasionally, until falling apart and much of the liquid has evaporated, about 7 minutes.

Step 4

Stir in the tomato paste and cook, stirring constantly until brick red colored, about 1 minute. Stir in the wine and cook until the mixture is reduced, very thick and no smell of alcohol remains, 6 to 8 minutes. Add the broth and bring to a boil. Transfer to the bowl with the beef. Stir in the rice until completely combined. (The mixture will be wet.) Season with salt and pepper.

Step 5

Arrange a rack in the center of the oven and preheat to 450 degrees F.

Step 6

Place the peppers cut-side up in a 13-by-9-inch baking dish. Spoon the filling into the peppers, gently pressing it in with the back of a spoon. Be careful not to overstuff and split the sides of the peppers. Bake for 15 minutes. Then top with the cheese and continue baking until the filling is heated through and the cheese is browned in spots, 10 to 12 minutes.