Heat about 2 inches of oil in a large pot to 365 degrees F. Meanwhile, line a baking sheet with paper towels.
In a small bowl, stir together the Parmesan, sumac, cayenne and lemon zest.
Add the garlic to the oil. Fry until light golden, 30 seconds to 1 minute. Remove to the lined baking sheet to drain. Add half of the broccoli to the oil and fry, turning occasionally, until browned and crispy, about 3 minutes. Remove to the lined baking sheet to drain and season with salt. Repeat with the remaining broccoli.
Put the broccoli in a serving bowl and toss with the Parmesan mixture. Sprinkle with the fried garlic. Serve immediately with lemon wedges.