Heat grill to medium (350° to 450°). In a small bowl, whisk together yolk, garlic, and mustard. Starting with a thin drizzle and working up to a slow, steady stream, whisk in 1/4 cup each olive and vegetable oils to create a thick aioli, about 7 minutes. Whisk in 1/2 tsp. salt and chopped herbs; set aside.
Rub vegetables with remaining 1 tbsp. olive oil and sprinkle with remaining 1/2 tsp. salt. Grill zucchini, onion, pepper, and hot dogs, turning as needed, until vegetables are softened, grill marks appear, and hot dogs are slightly charred, 6 to 10 minutes. In the final few minutes, toast buns on grill. Thinly slice peppers and separate onions into rings. Gently stir together vegetables in a small bowl.
Spread herb aioli inside buns and add hot dogs. Top with vegetables and sprinkle with parsley and oregano leaves.
*Available at Whole Foods Market.