In a mini chopper, combine soy sauce, oil, lime juice, fish sauce, ginger, lemongrass, sugar and chopped Thai chile or serrano. Whirl to blend. Place in a dish with bok choy, scallions and whole Thai chiles, if using. Marinate 15 minutes.
Heat a gas grill to mediumhigh or the coals in a charcoal grill to medium-hot. Lightly grease grates.
Remove vegetables from marinade and reserve remaining liquid. Grill bok choy for about 4 minutes per side, and scallions and chiles (if using) for 2 to 3 minutes per side. Remove to a platter.
Place a grilling grid on grill and heat for a few minutes. Grill tomatoes and sugar snap peas on grid for about 5 minutes, turning frequently. Remove to platter with other vegetables; drizzle with reserved marinade. Serve with lime wedges for squeezing and, if desired, hot chili oil. Garnish with Thai basil, if desired.