Heat the oil in a saucepan. Add the onions and cook, stirring, until softened but don't let them brown.
Add the garlic and stir for another minute until it softens.
Add the turmeric, chilli powder, and black pepper. Stir in.
Add the broccoli florets and cook, stirring, until tender. Add the peas and stir them until softened. Add the water and bring to a boil.
Add the cooked potatoes and salt to taste.
Take the saucepan off the heat and blend the soup, either with a hand-blender or, very carefully, by transferring to a regular blender.
Transfer back to the saucepan and heat through. Add the almond milk at the end, if using.
Check the salt. Serve hot with some baked croutons.