Add all vegetables to a parchment-lined sheet pan or well-oiled cast-iron skillet. Top with the oil and spices. Toss until the vegetables are well coated.
Place the pan in the oven for 45 minutes, until the vegetables are soft.
Remove from the oven and allow to cool until safe to handle. Remove the garlic heads, then transfer the remaining contents of the pan to a high-speed blender. Squeeze the garlic cloves out of the heads and discard the skins. Add the almond milk to the blender. Combine until a smooth soup is formed, adding more milk or vegetable broth as desired.