Preheat the oven to 425°F and line a large baking sheet with parchment paper.
Pat the broccoli florets completely dry with paper towels, then place in a large bowl with the olive oil, minced garlic, salt, black pepper, and red pepper flakes, tossing until evenly coated.
Spread the broccoli in a single layer on the prepared baking sheet, making sure the florets aren't touching so they roast rather than steam.
Roast for 18-22 minutes, tossing once halfway through, until the edges are crispy and golden brown with some charred spots.
Remove from the oven and immediately sprinkle with the Pecorino Romano cheese, lemon zest, and lemon juice.
Toss gently to combine and serve immediately while hot.