Cut broccoli into small florets. Steam, blanch, roast or microwave for a few minutes. Do not overcook, maintaining a bright green appearance and crisp.
Melt butter in a large soup pot or dutch oven over medium heat. Add in onions, garlic, carrots, and celery. Sauteé for 8 to 10 minutes stirring to not over brown. Pour in wine bring to a boil reduce by half approximately 8 to 10 minutes. Whisk in flour stir until it makes a roux.
Stir in vegan broth, potatoes, nutritional yeast, mustard, and plant-based milk. Bring to a boil reduce heat cook until potatoes are fork-tender approximately 20 minutes.
Using a blender or food processor ladle soup into a blender, working in small batches, blend until smooth. Pour back into pot add in cooked broccoli and re-heat. Serve.
Sprinkle soup with vegan shredded cheese, fresh herbs, lemon zest, or roasted broccoli. You decide.