Begin by prepping your vegetables. Chop the broccoli (including the stems), carrots, and celery. Dice the onions, potatoes and mince the garlic. Set aside the broccoli florets.
Heat the olive oil in a large pot over medium heat. Add the onions, broccoli stems, carrots, celery, salt and pepper. Cook, stirring occasionally for about 10 minutes, or until the veggies soften. Add the garlic and stir for one more minute.
Add the potatoes, vegetable broth, and milk and stir to combine. Simmer for 20 minutes or until the potatoes are soft.
While the soup cooks, put the broccoli florets you had set aside in a steamer basket and place inside another pot with 1-inch of water. Bring the water to a simmer, cover, and steam the florets for about 5 minutes or until tender.
Next, transfer the soup to the blender, working in batches if necessary. Add the steamed broccoli florets, cashews, apple cider vinegar, mustard, dill, and lemon juice and blend until you reach your desired consistency. Water can be added to thin the soup if you're finding it's too thick for your liking.
Season to taste and serve with your favorite garnishes! Try nutritional yeast for an extra cheesy punch, a few spigs of parsely, or a dollup of vegan sour cream.