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

Prepare a medium-hot fire in a charcoal or gas grill. Put bok choy stalks in a large bowl. Using your hands (or a fork), coat bok choy with miso butter. Arrange bok choy, cut side down, on 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 lid and grill for about 5 minutes, until golden brown on the underside. Turn bok choy with tongs, re-cover, and grill for 5–6 minutes more, until golden and crisp-tender.

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

Put grilled bok choy on dressed salad to wilt leaves; sprinkle with additional salt and pepper. Serve immediately.