Bring a large pot of salted water to a boil over high heat. Add potatoes and cook just until tender, about 7 minutes. Do not cook to mush. Drain. Set aside.
In a small bowl combine vinegar, mustard, mayonnaise, sugar, salt, pepper, and cannabis oil. Whisk to combine.
Place drained potatoes in a large bowl along with the celery, onion, hard-boiled eggs, and Italian parsley. Add the dressing and toss gently to combine and evenly mix and coat all the ingredients. Chill until ready to serve.