The butter should be melted in a large pot on medium heat. Add the chopped onion and cook it for 3-4 minutes until it becomes soft and clear. Add the garlic and cook 30 seconds; no longer.

Add the flour and stir continuously after a span of 2 minutes. This is your thickener! It will enrich the soup and make it velvety. The blend will be somewhat paste-like - that is not at all unusual.

Add slowly the chicken broth and you do not need lumps so you have to do it gradually. Add the cut broccoli, then simmer, then cook uncovered and after approximately 10-12 minutes, the broccoli is tender.

Unless you want your soup to be absolutely smooth, purée it a little, only partially using an immersion blender. Keep some chunks of broccoli for the texture.

Lower the heat to medium-low. Add milk and cream very slowly and stir it. Next, put shredded cheddar cheese in handfuls and stir until it is smooth and melted.

Salt, pepper, nutmeg, and smoked paprika. Add salt and taste according to taste - each cheese is salty to a different degree.

Pour the soup into bowls, sprinkling over it a little more cheddar, and serve with hot bread or crackers.