Light grill and set up for high direct heat on one side and low on the other.
Using a sharp knife, slice bok choy in half lengthwise. Set aside.
Place a saucepan over low heat on grill and melt butter. Add olive oil, garlic, ginger, and red pepper flakes to the melted butter and whisk together. Cook for 5 minutes until flavors are fully incorporated.
Spoon the melted butter and oil mixture over the halved baby bok choy. Grill cut-side down over high direct heat for 3 minutes. Turn and grill opposite side for 3 minutes or until you achieve a nice char.
Remove from grill and sprinkle a pinch of kosher salt on each half. Serve hot.