Place the parsley in a large bowl and cover with enough cold water to fully submerge. Swish it around to let any dirt fall to the bottom. Remove the parsley to a salad spinner and spin dry. If you don't have a salad spinner, sandwich the parsley between several layers of paper towels, and press firmly until almost dry.
Pick the leaves and discard the stems. You should have approximately 3 ounces of leaves.
Whisk the lemon zest, juice, walnut and sesame oils, honey, 1/2 teaspoon of the salt, and 1/2 teaspoon of the pepper in a large mixing bowl. Add the parsley leaves and toss to combine, using your hands to evenly coat. Cover the bowl with plastic and refrigerate for at least 30 minutes to allow the flavors to meld.
In the meantime, finely chop the walnuts to a coarse bread crumb consistency. Add the nuts, sesame seeds, and remaining 1/2 teaspoon of salt to a 10-inch skillet over medium-low heat. Toast the mixture for 7 minutes, tossing and stirring frequently, until it's deeply golden brown. Remove to a plate to cool.
Retrieve the parsley salad from the fridge, toss with the cooled nut mixture and a few grinds of fresh black pepper and serve.