Whisk together sesame oil, salt, and pepper in a large bowl. Add shishito peppers and toss to coat. Let sit for 10 minutes.
Whisk mayonnaise, soy sauce, sesame oil, and garlic together in a small bowl. Refrigerate aioli until ready to use.
Preheat an outdoor grill for medium-high heat. Toss shishito peppers in the marinade and transfer to a grill basket. Cook for 5 minutes, flipping peppers with tongs every 1 to 2 minutes to get an even char. Serve with aioli for dipping.