Melt the butter in a large Dutch oven over medium heat.
Add the diced onion and cook until translucent and soft.
Whisk in the flour and cook for two minutes to eliminate the raw flour taste.
Pour in the vegetable broth and milk slowly while whisking constantly.
Simmer the mixture until the liquid thickens enough to coat the back of a spoon.
Stir in the garlic powder, salt to taste, and nutmeg.
Add the broccoli florets and cook until they reach a tender texture.
Reduce the heat to low to prevent the milk from curdling.
Fold in the grated cheddar cheese one handful at a time until fully melted.