Drizzle cut side of bok choy with 1 tablespoon of the sesame oil and rub all over to coat. Place cut side down on grill and close cover. Cook 6 minutes; turn and cook 6-8 minutes more until crisp-tender with lightly charred areas. Arrange on serving platter cut side up.
Heat remaining tablespoon of sesame oil in a small skillet over medium-high heat. Add garlic and ginger; cook and stir until fragrant, about 30 seconds. Remove from heat and stir in chili paste, soy sauce and toasted sesame oil. Drizzle evenly over grilled bok choy. Garnish with toasted sesame seeds if desired and serve.
If you want to avoid the char on the tender leaves, you can place a strip of foil on your grill under just the leaves, leaving the remainder of the bok choy over direct heat.