Heat olive oil in a large pot over medium heat. Add onions and a pinch of salt. Cook, stirring occasionally, until onions are soft and translucent, about 10 minutes.

While onions cook, make seasoning mixture: Whisk together white wine vinegar, miso paste, Dijon mustard, and salt in a medium mixing bowl. Add nutritional yeast and arrowroot powder; whisk to incorporate. Start with ¼ cup soy milk and whisk until completely smooth. Continue adding soy milk in small increments, whisking thoroughly between each addition, until all milk is incorporated into a smooth slurry.

Add diced potatoes to pot with onions. Pour in seasoning slurry and water. Bring mixture just to a boil, then reduce heat to maintain a gentle simmer. Cover and cook for 15 minutes.

Add broccoli florets to pot. Continue simmering for 20 minutes, or until both potatoes and broccoli are tender when pierced with a fork.