Whisk together sesame oil, soy sauce, ginger, and garlic in a large bowl. Add shishito peppers and toss to combine. Let marinate for 15 to 20 minutes, tossing occasionally.

Preheat an outdoor grill for medium-high heat and heat a grill pan.

Remove peppers from marinade, letting excess marinade drip back into the bowl. Place peppers on the grill pan and cook, tossing every 1 to 2 minutes, until evenly charred, 5 to 7 minutes. Return peppers to bowl with marinade and toss. Sprinkle with salt, if desired, and serve.