Preheat the oven to 400°F (200°C). Line a large baking sheet with parchment paper.
Place the pumpkin, potatoes, and red onion onto the baking sheet. Nestle the garlic head (cut side up) among the vegetables.
Drizzle the vegetables and garlic with 2 tablespoons of olive oil. Sprinkle with cumin, garam masala, curry powder, ground coriander, turmeric (if using), red pepper flakes (if using), salt, and pepper. Toss everything well with your hands, making sure the garlic stays upright.
Roast for 35–40 minutes, or until the vegetables are tender and golden brown. The garlic should be soft and caramelized.
While the vegetables roast, toss the torn sourdough bread with a drizzle of olive oil and a pinch of salt. Spread onto a small tray and bake during the final 10–12 minutes of roasting, until golden and crisp.
Squeeze the roasted garlic cloves out of their skins. Transfer the roasted vegetables and garlic to a high-speed blender along with the coconut milk, drained white beans, soy sauce, and 2 cups of vegetable broth. Blend until smooth, adding more broth as needed to reach your desired consistency.
If the soup has cooled, pour it into a large pot and heat gently over low until warmed through. Taste and adjust seasoning with extra soy sauce or salt as needed.
Ladle the soup into bowls and garnish with coconut yogurt or cream, toasted pumpkin seeds, sourdough croutons, and chopped cilantro or parsley. Finish with a drizzle of olive oil if desired.