Don't even think about throwing out your broccoli stems. Use a mandoline to slice vegetables into planks, then stack and slice crosswise with a knife for a julienned cut.
In a small bowl, whisk together mayonnaise, olive oil, lemon juice and mustard. Season with salt and pepper.
In another bowl, combine broccoli, celery and apple. Pour over dressing and toss to combine. Season with salt and pepper. Serve.