Heat the oil in a large soup pot over medium-low heat. Add the onion and sauté, stirring occasionally, until golden, 8 to 10 minutes.

Add the sweet potatoes, carrots, and just enough water to barely cover the vegetables (about 4 cups).

Bring to a slow boil over medium-high heat, then stir in the tomatoes, bay leaves, all-purpose seasoning, cinnamon, and basil or oregano. Reduce the heat, cover, and simmer gently until the sweet potatoes and carrots are tender, 20 to 25 minutes. Remove and discard the bay leaves.

If using an immersion blender, add the beans to the pot and blend about half of the soup right in the pot, leaving plenty of chunks for texture.

If using a food processor or blender, transfer about half of the solid ingredients to the container along with half of the beans and a little of the cooking liquid. Process until smooth, then return the purée to the soup pot and stir in the remaining beans.

Stir in enough nondairy milk to give the soup a slightly thick consistency, starting with 1 cup. Season with salt and pepper, then simmer over very low heat for 10 minutes longer.

Serve at once, or let stand off the heat for an hour or two before serving, then heat through as needed. Top individual servings with parsley or cilantro, if desired.