Preheat grill to Medium-High and brush grill grates with oil.
In a saucepan set over medium heat, combine soy sauce, sesame oil, garlic, and sugar; whisk and bring to a simmer, stirring frequently, until it begins to thicken. Remove from heat. Set aside.
Cut the zucchini into long 1/4-inch thick strips.
Place zucchini on the hot grill in one single layer.
Close the lid and cook for 3 minutes.
Using tongs, flip over the zucchini; cover and continue to cook for 2 to 3 more minutes, or until charred and tender. Remove from heat.
Remove from heat and brush each slice of zucchini with the sauce.
Garnish with sesame seeds and pepper flakes. Serve.