Set a rimmed baking sheet on an oven rack and preheat to 425 degrees F.
Add the broccoli, oil, garlic, shallots, 3/4 teaspoon salt and red pepper flakes to a large bowl and toss to coat. Transfer to the preheated baking sheet and spread out in a single layer. Roast until the broccoli florets are browned on the ends, the stalks are crisp-tender and the shallots are caramelized, about 20 minutes, tossing about halfway through. Immediately sprinkle with the Asiago and lemon zest. Season with some salt if needed. Transfer to a serving platter.
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