Preheat the broiler. Place the pork on a rimmed baking sheet; season generously with salt and pepper. Mix 1 tablespoon olive oil, the grated garlic, paprika, oregano and 1 teaspoon Peppadew brine in a bowl; rub all over the pork and set aside 5 minutes. Broil the pork until lightly browned, about 8 minutes.
Meanwhile, toss the broccoli, chickpeas, Peppadews, whole garlic cloves, 2 tablespoons olive oil, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Remove the pork from the oven and flip. Spread the broccoli mixture around the pork. Continue broiling until a thermometer inserted into the pork registers 145 degrees F and the broccoli is lightly charred, 6 to 9 more minutes. Transfer the pork to a cutting board and let rest 10 minutes.
Squeeze the broiled garlic cloves from their skins; finely chop. Combine the garlic with the remaining 2 tablespoons olive oil and 2 teaspoons Peppadew brine, the parsley, lemon zest and juice and a pinch of salt in a small bowl. Slice the pork and serve with the broccoli mixture. Drizzle the herb sauce on the pork.