Peel a sweet potato and cut it into cubes (spending time cutting it smaller will save time needed to boil them). Place it in a big pot.
Dice the onion and mince the garlic, then add it to the pot together with the water and bring to boil. Lower the heat, cover and let it simmer for 20 min.
If the broccoli florets are big then cut them in half and place on an oven sheet pan lined with parchment paper. Season well with salt and pepper. Place in the oven for around 15 min. The tips of the broccoli should start to get brown when it is ready.
Add the coconut milk to the soup. Shred the cheese and clean up while waiting
Use a hand immersion blender to mix the soup smooth, add the liquid smoke and shredded cheese and stir to melt the cheese and blend it well.
You might want to season with more salt and pepper here then serve with the roasted broccoli and a slice of bread