To make sure the veggies are soft, cover and simmer for at least four to six hours, or cook them for two to three hours on high.
Incorporate the Cream Base:

In a small bowl, mix the flour and cream until smooth, about half an hour before serving.
Stir the cream mixture before pouring it into the crockpot. The soup will thicken as a result of this.
Garnish with Cheese:

While stirring continuously, slowly incorporate the Parmesan and shredded cheddar cheese into the soup until it thickens and the cheese melts.
Toss in the ground mustard and paprika, if you want.
When it is:

Season with salt and pepper to taste.
Combine (Not Required):

Alternately, you may purée some of the soup in a blender before putting it back into the crockpot, or you could use an immersion blender to smooth down the soup. If desired, you may save a few broccoli and carrot bits for texture.
Place the order:

When the soup has thickened to your liking and the cheese has melted, it's time to dig in. Spoon into serving dishes and enjoy!
Add more heavy cream or half-and-half just before serving if you want it extra creamy.
Add some toppings like chopped fresh parsley, paprika, or additional cheddar cheese.
Put any leftovers in a sealed jar and refrigerate for no more than three days. Gently reheat in the microwave or on the stovetop.
With some crusty bread or a side salad, this soup is the ideal comfort food on a chilly day. Soup with broccoli and cheese—enjoy!