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Pat the shrimp dry and season with a big pinch of kosher salt, black pepper and red pepper flakes. Drizzle with extra virgin olive oil and toss to be sure the shrimp is well-coated with the oil.
In a large bowl, combine garlic, parsley (if using), lemon juice and zest, ¼ cup extra virgin olive oil, oregano, and red pepper flakes. Season lightly with salt and pepper. Whisk together.
Heat a grill or indoor griddle to medium-high and lightly oil the grates. Grill the shrimp on each side until just pink (about 5 minutes or so in total, depending on the size of the shrimp).
Immediately remove the shrimp from the heat and toss it in the prepared olive oil and garlic mixture. Add the parmesan cheese, then toss to coat.
Transfer to a serving plate and serve immediately.