Heat 1 tablespoon extra-virgin olive oil in a saucepan over medium heat and sauté the minced garlic for about 1 minute until fragrant.
Add the canned diced tomatoes with their liquid to the pan, bring to a boil, then reduce heat to a simmer.
Season the sauce with 1 1/4 teaspoons dried oregano, 1/2 teaspoon salt, and 1/4 teaspoon black pepper, then simmer for 10–15 minutes until slightly thickened.
Preheat the oven to 375°F (190°C). Grease a 13 x 9-inch baking dish and pour 1 cup of the sauce into the bottom; set aside.
In a mixing bowl, combine the grated Parmesan, 2 cups shredded part-skim mozzarella, 1/2 cup ricotta, 1/4 teaspoon pepper, and 1 teaspoon dried oregano; reserve 1/2 cup of this cheese mixture for the topping.
Spread about 1/2 cup of the cheese mixture evenly over each cooked lasagna noodle (reserve 1/2 cup total), drizzle 1 tablespoon of sauce over the cheese on each noodle, then roll each noodle tightly and place seam-side down in the prepared baking dish.
Pour 1 1/2 cups of the remaining sauce over the rolls and sprinkle the reserved 1/2 cup cheese mixture evenly on top.
Loosely cover the dish with foil and bake for 25–30 minutes, until the cheese is fully melted and the filling is hot.
Let the rolls rest for a few minutes before serving.