Add garlic, water, caper brine, olive brine, salt and pepper to a food processor or blender; pulse until garlic is crushed.
Place the pork chops in a hotel pan and pour the brine over the pork chops. Cover and refrigerate for 24 hours. Remove pork chops from brine and discard the brine. Pat dry with paper towels and refrigerate up to 2 days.
For the Dry Rub
Whisk all ingredients in a small bowl until combined.
For the Spanish Olive-Caper Sauce
Sauté the onion, olives, capers and garlic in olive oil in a large sauté pan over high heat 1 minute. Deglaze the pan with the sherry and cook for 30 seconds. Stir in lemon juice, salt and pepper.
Remove pan from the heat; stir in extra virgin olive oil, parsley and oregano.
Sprinkle pork chop liberally with the dry rub and coat with olive oil. Grill pork chop for 4 minutes over high heat, rotating the pork chop 45 degrees after 2 minutes to create crosshatch marks. Turn pork chop and repeat on the second side, cooking until the internal temperature reaches 145°F.
Place 1 cup warm seasoned quinoa on serving plate. Angle pork chop on top and spoon Spanish Olive-Caper Sauce over the top. Garnish with lemon slices.