In a small saucepan, bring the EVOO, sage leaves, halved garlic and kosher salt to a gentle boil over medium. Reduce the heat to medium-low and simmer until the sage is crispy and the garlic begins to brown, about 5 minutes. Strain the oil into a small bowl; discard the garlic. Transfer the sage leaves to paper towels; let cool, then crumble and reserve. Stir the 2 tbsp. chopped sage into the infused oil.
Preheat a grill to medium-high. Brush the bok choy all over with the garlic-sage oil. Grill, turning once, until the leaves are charred in spots and the bulbs are crisp- tender, about 12 minutes. Arrange cut-side up on a platter; season with salt and pepper. Drizzle with the lime juice and sprinkle with the crumbled sage leaves.