Peel and dice the onions and potato into small-medium pieces and mince/grate the garlic. Crumble or grate the cheese, depending what kind you have.
Warm the oil in a medium pot/saucepan over a medium heat. Add the onion to the pot/pan and cook, stirring now and then, for around 3 - 5 minutes until the onions are softened and translucent. It's fine if they brown slightly, but don't let them burn - reduce the heat and/or add a little extra
Add the cumin, achiote, salt and a little pepper to the pot and stir to mix everything through. Cook for a minute or two then add the potatoes. Mix through well and cook a minute more, stirring regularly so the spices and vegetables don't burn.
Add the water, using a little more if needed, so that the potatoes are just covered with water. Cover the pot/pan and bring to a boil. Reduce the heat to a moderate simmer and cook for round 20 - 30 minutes until the potatoes are very tender - they should break up easily when you press against the side of the pot.
Remove from the heat and blend up the soup. You can either completely blend until smooth or leave some of the potato in chunks, as is more traditional. Add the milk, mix through then add in the cheese. Mix both well so that they blend into the soup. Check the seasoning and add additional salt/pepper to taste. If needed, reheat a little before serving.
Serve with garnishes of your choice - a little extra cheese, some sliced or diced avocado and some cilantro/coriander are pretty typical. You could also add some chili/hot sauce.