Make the pork loin: Preheat the oven to 425 degrees F.
Place the first 5 ingredients in the bowl of a mini chopper. Process until the mixture resembles a coarse paste. Rub the paste over the surface of the pork and allow the pork to sit for 30 minutes at room temperature, or in the refrigerator for up to 6 hours¿leave roast at room temperature for 30 minutes before roasting if refrigerated. Roast the pork for 30 to 50 minutes, check temperature with a meat thermometer. The temperature should read 140 degrees F. Remove the pork as soon as it reaches the correct temperature, cover with foil and let rest for 15 minutes.
Make the succotash: Place the beans in a saucepan and cover with salted water. Simmer until tender, 6 to 8 minutes for frozen beans, and 25 minutes for fresh shelling beans. Drain the beans, and using the same saucepan, add the butter and the corn and saute quickly, about 2 minutes. Add the cream, sugar, beans, and salt and pepper. Cook over low heat for about three minutes more.
Spoon the succotash into 6 shallow bowls, sprinkle with paprika and parsley. Top each with 3 to 4 (1-inch) slices of the pork loin and serve immediately.