Cut up cauliflower into same-sized pieces and steam until fork-tender, about 5-10 minutes (depending on the size of your florets). Drain and place into a large bowl; let cool to room temperature.
While cauliflower is steaming, boil the eggs. Place in a small saucepan and cover with cold water. Bring to a boil, lower the heat, and cook for 6-7 minutes. Cool, peel, and slice or chop.
Add chopped celery, green onions, eggs, and chopped parsley to the bowl with the cauliflower.
In a small bowl, make the dressing: whisk the mustard, oil, vinegar, and salt together until combined. Gently fold with the cauliflower. Chill before serving.
Notes
Want to make this salad a main dish? Load it with crispy bacon, shredded cheddar, and add mayo and sour cream to the dressing!