Preheat oven to 350 degrees F (180 degrees C). Scatter the Walnut (3/4 cup) onto a jelly-roll pan and roast for 5-10 minutes, until deep golden brown.
Pour the nuts into a tea towel and rub well to remove as much skin as possible. Chop the walnuts coarsely and toss in a sieve to remove any remaining skin or dust.
Combine Italian Flat-Leaf Parsley (1 tablespoon), Serrano Chili (1), Shallot (2), Shelled Unsalted Pistachios (1/4 cup), Green Olives (1/2 cup), Lemon (1/2), walnuts, Pomegranate Seeds (1/2 cup), Extra-Virgin Olive Oil (1 tablespoon), Walnut Oil (1 tablespoon), Sea Salt (to taste), Ground Black Pepper (to taste) in a large bowl and toss gently.
Leave to stand for 5 minutes or so before serving to allow flavors to meld. Taste and adjust seasoning as necessary — add more lemon, olive oil, pepper, salt.