Preheat your oven to 425 degrees F and position a rack in the center. A properly hot oven is the key to roasting rather than steaming, so give it a full 15 minutes to come up to temperature.

If you just washed the broccoli, dry the florets thoroughly with a clean kitchen towel or paper towels. Wet broccoli will steam in the oven and you will not get crispy edges.

Spread the florets across a large rimmed sheet pan. Drizzle the olive oil over them, then scatter the minced garlic, salt, black pepper, and red pepper flakes if using. Toss everything together right on the pan until the florets are evenly coated.

Arrange the broccoli in a single layer with the flat cut sides facing down against the pan. If the pieces are touching each other all over, use a second sheet pan. Crowding is the enemy of crispiness.

Roast for 18 to 20 minutes, until the stem pieces are tender when poked with a fork and the floret edges are deeply golden and just a little crisp. Do not stir them partway through, letting that flat side stay in contact with the pan builds the brown crust.

Pull the pan out of the oven and immediately scatter the grated Parmesan over the hot broccoli. The residual heat melts it right in. Taste and add a small pinch more salt if needed, then transfer to a serving dish and bring it straight to the table.