Mix the milk, water, and turmeric together and set aside.

Melt the butter in a large pot then add the flour.

When the flour starts turning white, add the milk mixture.

Stir until the mixture has thickened. It should be thick enough to stick to the back of a spoon. If it is not thickening enough, add a tablespoon more flour.

When the mixture has thickened, add the mashed potatoes and stir them so they mix in well.

Add the cheese and stir that until it has melted.

Add the broccoli and break it up with your hand as you do.

Use a stick blender or pour the soup into a blender to completely break up the broccoli.

Add the grated nutmeg and stir to combine.

Serve with pimento cheese toasts.