Preheat oven to 400 degrees. If using fresh broccoli, steam in a microwave-safe dish by adding a few tablespoons water, covering with a lid, and microwaving 2-4 minutes until bright green and crisp-tender. If using frozen, thaw and squeeze out as much liquid as possible. Place steamed or thawed broccoli in the bowl of a food processor and pulse until finely chopped (but not pureed).
In a large bowl, mix chopped broccoli, ricotta, 1 c. mozzarella, 2 Tbsp. Parmesan, garlic powder, oregano, basil, salt, and pepper.
In a medium bowl, stir half and half into marinara sauce.
Assemble lasagna: in an 8-inch square baking dish, spoon a thin layer of sauce. Top with two noodles, a quarter of remaining sauce, and a third of the broccoli mixture. Repeat twice. Top with the remaining two noodles and sauce. Sprinkle the top with remaining 1/4 c. mozzarella and 2 Tbsp. Parmesan.
Cover tightly with aluminum foil and bake 35-40 minutes. Uncover and bake an additional 10-15 minutes.