Heat oven to 425ºF.
Cut the broccoli florets into bite-size pieces. Peel the stalk and cut into 1/8-inch-thick, round slices. Place the broccoli into a mixing bowl and toss with the olive oil, garlic, salt, and pepper and set aside.
Spread the panko on a half sheet pan and bake until lightly toasted, about 2 minutes. Remove the panko from the oven, pour into a second bowl, and set aside.
Pour the broccoli onto the now hot half sheet pan and roast for 8 minutes. Remove the broccoli from the oven, toss with the toasted panko, and return to the oven until the broccoli is tender, about 12 minutes more. Remove from the oven, toss with the cheese and serve immediately.