Heat the oven to 375°F and grease a deep, roughly 3-quart oval baking dish or deep casserole dish with nonstick spray or a little oil.

Warm the tablespoon of oil in a large skillet over medium-high heat, add the ground beef, sprinkle with kosher salt and black pepper, and cook for 6 to 8 minutes, breaking it up and stirring occasionally, until no pink remains and most of the moisture has cooked away; drain excess fat if needed.

While the beef cooks, chop the green bell peppers into noticeable bite-size pieces that are not too tiny and not oversized.

In a large mixing bowl, stir together the uncooked pasta, uncooked rice, and chopped peppers, then add the cooked beef, the entire jar of sauce, and all 4 cups of water.

Stir the mixture very thoroughly, scraping down to the bottom of the bowl so no dry rice or pasta is hiding, and taste a tiny spoonful of the liquid to add more salt or pepper if needed.

Pour everything into the prepared baking dish, smooth it out so the pasta and rice are mostly submerged, and cover the dish tightly with foil, crimping around the edges to trap steam.

Bake covered for 45 to 55 minutes, starting to check around 40 minutes, until the rice and pasta are tender; if either still has a firm core, cover again and bake another 5 to 10 minutes.

When the pasta and rice are tender and the liquid has cooked down into a thick sauce, remove the foil and scatter the mozzarella evenly over the top, leaving a few small gaps.

Bake uncovered for another 10 to 15 minutes, until the cheese is melted, bubbling, and browned around the edges; for more color, broil for 1 to 2 minutes while watching closely.

Let the casserole rest for at least 10 minutes before scooping so it thickens and portions hold together better, then serve from the dish with a green salad, garlic bread, or a crusty baguette.