In a large saucepan, combine the chicken broth, water, dried minced onion, parsley, and oregano. Bring the mixture to a boil over medium-high heat. Once boiling, reduce the heat and let it simmer for about 5 minutes to allow the flavors to meld.

Slowly add the melted butter to the simmering broth, stirring continuously. Gradually sprinkle in the flour while stirring to prevent lumps from forming. Continue to stir until the mixture thickens slightly, forming a smooth roux.

Stir in the salt and black pepper to season the soup base. Pour in the half-and-half, continuing to stir to maintain a smooth consistency. Increase the heat slightly and cook until the mixture becomes bubbly and starts to thicken, ensuring you stir frequently to prevent scorching.

Add the cubed potatoes to the soup. Reduce the heat to low and cover the saucepan. Let the soup simmer gently for about 1 hour, or until the potatoes are tender when pierced with a fork. Stir occasionally to prevent the soup from sticking to the bottom of the pan.

Once the potatoes are tender and the soup has reached a creamy consistency, remove it from the heat. Ladle the hot soup into bowls and garnish with your choice of toppings.