Melt the butter in a saucepan and add the chopped onions. Saute until soft.

In a large stock pot, bring the water to a boil and add the potatoes, cooking them until they are just tender.

Darin the water, but keep 1 cup of it, setting it aside.

Stir in the melted butter and onion with the potatoes, add the flour.

Stir well. Add the reserved water and milk and bring to a simmer.

Add the shredded cheese a little at a time mixing it in well.

Simmer for 30 minutes, stirring frequently.

Add salt & pepper to taste.

Sprinkle the top with paprika and serve with chopped green onions or cilantro.