Preheat the oven to 375°F (190°C). Lightly grease a deep oval baking dish (about 3-quart capacity) with nonstick spray or a little oil. This shape helps mimic that classic neighborly casserole look and makes it easy to scoop with a wooden spoon.
In a large skillet over medium-high heat, warm the olive oil. Add the ground beef, breaking it up with a wooden spoon. Season with 1 teaspoon kosher salt and 1/2 teaspoon black pepper. Cook, stirring occasionally, until the beef is no longer pink and any excess moisture has mostly cooked off, 6–8 minutes. Drain off excess fat if needed to keep the bake from becoming greasy.
While the beef cooks, chop the green bell peppers into bite-size pieces. You want them large enough to stay distinct in the bake, like traditional stuffed pepper chunks, but not so big that they dominate each bite.
In a large mixing bowl, combine the uncooked pasta, uncooked rice, and chopped green peppers. Stir to distribute everything evenly. This dry mix will soak up the sauce and water in the oven, giving you that stuffed-pepper rice texture along with tender pasta.
Add the cooked ground beef to the bowl with the pasta, rice, and peppers. Pour in the entire jar of tomato pasta sauce and the 4 cups of water. Stir very well, making sure there are no dry pockets of pasta or rice stuck at the bottom of the bowl. The mixture will look quite loose and soupy at this point—that’s what you want for the pasta and rice to cook through in the oven.
Taste the liquid (just a small spoonful) and adjust the seasoning with a bit more salt and pepper if desired, remembering that the cheese will add some saltiness later.
Pour the mixture into the prepared deep oval baking dish, smoothing it into an even layer so the pasta and rice are submerged in the liquid. Cover the dish tightly with foil, crimping the edges to keep steam in; this is crucial for cooking the rice and pasta all the way through.
Bake, covered, for 45–55 minutes, until the rice and pasta are just tender. Begin checking around the 40-minute mark by carefully removing the foil and tasting a small spoonful from the center. If the pasta or rice still has a firm core, recover and continue baking in 5–10 minute increments.
