Heat 1 Tbs extra virgin olive oil in a large pot over medium heat. Add 1 cup diced 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 1 Tbs white wine vinegar, 1 Tbs white miso paste, 1 Tbs Dijon mustard, and 1 tsp sea salt in a medium mixing bowl. Add ½ cup nutritional yeast and 2 Tbs arrowroot powder; whisk to incorporate. Start with 2 Tbs soy milk and whisk until completely smooth. Continue adding soy milk in small increments, whisking thoroughly between each addition, until all 1 cup soy milk is incorporated into a smooth slurry.
Add 1 cup diced potatoes to pot with onions. Pour in seasoning slurry and 2 cups water. Bring mixture just to a boil, then reduce heat to maintain a gentle simmer. Cover and cook for 15 minutes.
Add 2 cups broccoli florets to pot. Continue simmering for 20 minutes, or until both potatoes and broccoli are tender when pierced with a fork.
Remove pot from heat and let stand for 10 minutes before serving.