Peel and trim off the ends of the sweet potatoes. Chop as small as you have the patience and dexterity for, knowing that the smaller you cut the cubes the faster they'll cook and the easier they'll blend.

Bring to a boil over high heat and then reduce the heat so it simmers, not too aggressively but not too gently either - it should be bubbling fairly quickly with small bubbles. Depending on the size of the sweet potato cubes, they should soften enough in 12-18 minutes. If a fork easily slides through one, it's ready.

Blitz to a smooth puree using an immersion blender. I find this much easier than using a blender, plus immersion blenders are relatively cheap and don't take up as much room. But if you only have a blender, fill it no more than halfway full, put the lid on but take out the inner cap, hold a towel over the hole in the lid (all of this is necessary to contain the hot liquid which will expand when you turn it on), and blend until smooth. Pour into a bowl, add more of the soup to the blender and continue this process until it's done.