Cut the leaves away from the bok choy stalks. Halve the stalks lengthwise. Rinse the leaves and stalks well, then pat dry to remove any excess water. In a small bowl, mix together the butter and miso with a fork until well combined. Set aside.

Prepare a medium-hot fire in a charcoal or gas grill. Put the bok choy stalks in a large bowl. Using your hands (or a fork), coat the bok choy with the miso butter. Arrange the bok choy, cut side down, on the grill grate. (If you have a grill screen, set it on top of the grate before adding the bok choy, to keep the stalks from falling through the gaps.) Close the lid and grill for about 5 minutes, until golden brown on the underside. Turn the bok choy with tongs, re-cover, and grill for 5 to 6 minutes more, until golden and crisp-tender.

While the stalks are cooking, stack the bok choy leaves and roll them up lengthwise into a cigar shape. Slice the leaves crosswise into thin shreds. Make a bed of the shredded leaves on a serving platter. Drizzle the leaves with the oil and lemon juice, sprinkle with the salt and 1/4 teaspoon pepper, and toss to combine.

Put the grilled bok choy on the dressed salad to wilt the leaves; sprinkle additional pepper over the bok choy. Serve immediately.