Preheat oven to 375 degrees and line a rimmed baking sheet with parchment paper. Cut cauliflower and broccoli into florets and place in a large mixing bowl. In a separate small bowl, whisk together the gochujang, kosher salt, and olive oil.
Add the gochujang mixture to the vegetables and give it a toss to coat the vegetables in the mixture. Layer onto the prepared baking sheet.
Roughly chop the spring onion, peeled shallots, and peeled garlic cloves and add to the rimmed baking sheet with vegetables. Roast for about 25 to 30 minutes until fork tender and edges slightly begin to caramelize.
While the vegetables roast, make the Miso-Gochujang sauce. Whisk together the white miso, gochujang, maple syrup, and rice vinegar until smooth.
Once vegetables are ready, remove from oven and allow to cool slightly for 5 minutes. Add half the vegetables to a blender pitcher along with a heaping cup of the canned white beans.
Add in vegetable stock then blend until smooth. Pour the soup into a heavy bottomed pot to simmer slightly and add remaining unblended vegetables and beans to the pot. Allow soup to warm through. Ladle soup into bowls and drizzle with the Miso-Gochujang Sauce.