In a medium pot, mix together water, vinegar, onion, garlic, lemon juice and zest, salt, sugar and peppercorns, and bring to a simmer over medium-high heat. Transfer liquid to shallow baking dish and add the ice cubes. Let sit for 10 minutes. Once ice has melted and liquid has cooled completely, lay in the chops, cover, and refrigerate for 4-6 hours.
Meanwhile, place arugula, walnuts, lemon juice and garlic in a food processor and pulse while slowly pouring in oil until it forms a smooth paste. Spoon into a small bowl, season to taste with salt and pepper and set aside.
Preheat oven to 375°F. Remove pork chops from brine and pat dry. Pan-sear the chops in an oven-safe skillet over medium-high heat, then finish in oven for about 8 minutes, or until a thermometer inserted into the thickest part of the chop reads 150°F (65°C). Let pork rest for 10-15 minutes before serving topped with arugula pesto.
Yield: 5-6
Total time: 6 h 20 min
Prep Time: 360 Minutes
Cooking Time: 20 Minutes
Total Time: 380 Minutes