Bring water to a boil in a saucepan; remove from heat and stir couscous into the water. Cover saucepan and let stand until water is absorbed completely, 5 to 10 minutes. Fluff couscous with a fork.
Heat olive oil in a large skillet over medium heat; cook and stir onion in hot oil until onion starts to soften, about 5 minutes. Transfer 1/2 of the onion to a large bowl.
Pour marinara sauce, beef broth, balsamic vinegar, and red pepper flakes into skillet with remaining onion; cook and stir until heated through, about 1 minute. Pour marinara mixture into a 9x13-inch baking dish.
Stir vegan beef crumbles, diced tomatoes, parsley, garlic, black pepper, and cayenne pepper into onions in the large bowl until well-mixed. Add couscous and 3/4 of the Parmigiano-Reggiano cheese and stir until filling is well-combined. Stuff each pepper half with couscous mixture and place stuffed peppers in marinara sauce in the baking dish. Sprinkle remaining Parmigiano-Reggiano cheese over peppers and cover the baking dish with aluminum foil.
Bake in the preheated oven for 45 minutes. Remove aluminum foil and continue baking until peppers are tender and cheese is browned, 20 to 25 minutes more.