Steam potatoes for 20 minutes, remove and cool, then slice into bite-sized discs.
Place oil, parsley, green onions, lemon juice, mustard, and garlic into a food processor and process until emulsified. This will create your dressing.
Once the dressing mixture reaches desired consistency, drizzle over potatoes. Allow the dressing to be absorbed by the potatoes for a few hours if possible before serving, or refrigerate dressed potatoes overnight.
Prior to serving, add chopped celery to dressed potatoes and mix.
Top with additional parsley and green onions, toss again and serve.