Heat your oven to 450°F. This high heat is what gives you those beautiful caramelized edges.
Trim about an inch from the bottom of the broccoli stalk, then cut the florets into large, bite-sized pieces. Don't throw away those stalks - peel the tough outer layer with a vegetable peeler and slice them thin crosswise. My ayeeyo always said waste nothing, and broccoli stalks are sweet when roasted properly.
Divide the broccoli florets and sliced stalks between two large rimmed baking sheets. Add the sliced garlic, olive oil, and red pepper flakes, tossing everything with your hands to coat evenly. Season generously with coarse salt. (Don't crowd the broccoli on one sheet - it needs space to roast, not steam.)
Roast for 20 to 25 minutes, until the broccoli is crisp-tender with golden-brown edges. Halfway through, rotate the sheets from top to bottom and toss the broccoli once to ensure even browning.
Remove from the oven and immediately sprinkle with fresh lemon juice, tossing to coat. The acid brightens everything and balances the rich, nutty flavors.
Transfer to a serving platter and top generously with the grated Manchego. The cheese will soften slightly from the heat of the vegetables. Serve immediately while still warm.
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