Bring a large pot of salted water to a boil. Add the jumbo pasta shells and cook according to the package instructions until al dente (about 9 to 11 minutes). Drain, rinse with cold water, and set aside on a lightly oiled plate.
If using fresh broccoli, steam or blanch the chopped florets until just tender (3 to 4 minutes). If using frozen, thaw and drain excess water. Chop finely.
In a medium mixing bowl, combine ricotta cheese, shredded cheddar, grated Parmesan, beaten egg, garlic powder, onion powder, salt, and black pepper. Stir in the chopped broccoli until well incorporated.
Lay the cooked shells flat and spoon generous amounts of the cheese and broccoli filling into each shell without overfilling.
Preheat oven to 375°F (190°C). Spread 1 cup marinara sauce evenly in a 9x13 inch baking dish. Arrange stuffed shells in a single layer over the sauce. Pour remaining 1 cup marinara sauce over the shells.
Sprinkle shredded mozzarella evenly over the shells. Cover loosely with aluminum foil and bake for 25 minutes. Remove foil and bake an additional 10 minutes until cheese is golden and bubbly.
Let shells cool slightly before serving. Serve with salad or garlic bread if desired.