In a large soup pot, melt the butter and add the onions; cook for 5 minutes until softened.
Add chicken stock and potatoes; stir the soup
Set a timer for 10 minutes and turn the soup up to medium-high. It needs to boil, but not too hard.
Add the broccoli and 1/2 teaspoon of sea salt and set the timer for 10 more minutes.
When the timer goes off, add the cheese and stir until melted.
If the soup is not as thick as you'd like, mix 1/2 cup milk + 4 tbsp. flour and add it slowly, stirring constantly. You may not use it all. When the soup is thickened enough, stop.