Note:
Preheat oven to 425 degrees F.
Shave the stalk of the broccoli with a peeler. Cut the broccoli florets into bite-sized pieces, about 3/4 of an inch across. Cut the stalk into 1/4 inch thick, round slices. Place the broccoli into a mixing bowl and toss with the olive oil, garlic, salt, and pepper, and set aside.
On a large, rimmed baking sheet, add the broccoli mixture, sprinkle with the breadcrumbs and lightly toss.
Roast for 8 to 10 more minutes. Toss again. (Without being overly fussy, I try to push the stem portions towards the edges of the pan.) Roast five more minutes, or until broccoli is done to your taste.
Remove from the oven, while still hot, sprinkle with cheese and serve immediately.
Note: while still good the next day, this dish really is at its best when the bread crumbs are crispy and toasted. Feel free to modify the amount to suit your family.