Cut 1 pound of the Brussels sprouts in half. Doing so will cause some of the outermost leaves to fall off. Keep the loose leaves in a little pile on the cutting board.
Return the pan to the stove and heat over medium-high heat for 2 minutes. Add the remaining 4 tablespoons olive oil. Add the cut Brussels sprouts to the pan, arranging each one cut-side down. Cook, without stirring the sprouts, for 2 to 3 minutes or until sufficiently charred. Flip, season evenly with ½ teaspoon salt, and cook the rounded sides for another 2 minutes.
Add the reserved outer leaves and shake the pan to distribute. Cook for 10 more seconds, just to wilt the leaves, then transfer to a plate.
Shave the remaining raw Brussels sprouts thinly with a sharp knife, a mandoline, or a food processor fitted with a slicing/shredding blade. Toss the shaved Brussels sprouts into a large bowl. Add the pomegranate seeds, almonds, parsley, about three-quarters of the dressing, and ½ teaspoon salt. Toss to coat everything well. Taste, and adjust dressing and salt.
Thinly slice the remaining pear quarters. Serve the salad with pan-roasted Brussels sprouts and the sliced pears tucked in. Finish with squeeze of lemon juice, and a handful of parsley on top.