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1
Rub pork shoulder with 1/4 cup kosher salt. Set in rack in a baking dish, wrap in plastic wrap, and refrigerate for two to three days. When ready to cook, preheat oven to 475u00b0F and adjust oven rack to lower-middle position. Unwrap pork, pat dry with a paper towel, and roast until lightly browned, 35 to 40 minutes. Flip roast over, reduce heat to 300u00b0F, and continue to cook until center registers 170u00b0F on an instant read thermometer, 2 to 3 hours. Remove from oven and let rest for at least 45 minutes. Meanwhile, make the broccoli rabe.
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2
Bring a gallon of water to a boil over high heat. Add broccoli rabe and 2 tablespoons salt. Cook, stirring constantly until water returns to a boil, about 1 minute. Transfer broccoli to bowl of ice water and let sit 2 minutes. Drain well in a salad spinner and chop into 1-inch pieces. Transfer to medium bowl.
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3
Add garlic, pepper flakes, and olive oil to a small skillet and heat over low heat until garlic is sizzling, about 5 minutes. Pour garlic oil over broccoli rabe and toss to combine. Season with salt and pepper to taste, then stir in cheese. Slice pork as thinly as possible.
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4
Cut sandwich rolls in half and toast under the broiler or in a toaster oven. Lightly drizzle rolls with extra virgin olive oil. Top with pork followed by broccoli rabe. Close sandwiches, cut as desired, and serve.
