Preheat your oven to 350°F / 175°C.
Cook the manicotti shells according to package directions.
Drain well in a colander, rinse with cold water to stop the cooking process, and drain again. Carefully arrange the shells in a single layer on a sheet of foil to prevent them from sticking together.
While the pasta cooks, prepare the filling. Lightly coat a large nonstick skillet with cooking spray and preheat over medium heat.
Add the chopped mushrooms, shredded carrot, and minced garlic.
Sauté for 3 to 5 minutes, stirring occasionally, until the vegetables are just tender.
Remove from the heat and let it cool for a few minutes.
In a medium bowl, combine the slightly cooled vegetable mixture with the ricotta cheese, 1/2 cup (480 ml) of the mozzarella cheese, the beaten eggs, Parmesan cheese, and crushed Italian seasoning.
Mix until well combined.
Carefully spoon the cheese and vegetable mixture into each of the cooked manicotti shells. A small spoon or a piping bag makes this step easier.
To make the sauce, place the entire can of undrained diced tomatoes into a blender or food processor.
Cover and blend until smooth.
Pour the puréed tomatoes into a bowl and stir in the chopped roasted red peppers.
To assemble, spread about 1/3 cup (720 ml) of the sauce evenly over the bottom of a 2-quart rectangular baking dish (or divide it among four 12- to 16-ounce individual baking dishes).
Arrange the stuffed manicotti shells on top of the sauce, overlapping them slightly if needed.
Pour the remaining sauce evenly over the shells.
Cover the baking dish with foil.
Bake until heated through and bubbly. For individual dishes, bake for 20 to 25 minutes. For a single large dish, bake for 35 to 40 minutes.
Carefully remove the foil and sprinkle the remaining 1/4 cup (960 ml) of mozzarella cheese over the top. Return the dish to the oven and bake, uncovered, for 5 more minutes, or until the cheese is melted and golden.
Let the manicotti stand for 10 minutes before serving. This allows it to set, making it easier to serve.