Bring a large pot of water to a boil. Add the chicken breasts and boil until cooked through and most of the water has evaporated, about 25-30 minutes.
Place the boiled chicken breasts in a large bowl. Use a hand mixer to shred (or alternatively use two forks and hand shred). Season with salt, pepper and 3 tablespoons of paprika.
Pour out the water used to boil the chicken and return to the heat. Add two tablespoons of butter. When frothy, add the onions and stir until softened, about 3-4 minutes.
Add the tomatoes to the pot. Bring to a rolling simmer and cook until most of the liquid has evaporated. Stir in the flour to further absorb the liquid. Add the 1/3 cup of Hungarian paprika and stir until everything in the pot is covered.
Pour the broths into the pot. Bring a simmer for about ten minutes. Add the shredded chicken to the pot and heat through, about another 5-10 minutes. The soup should be bubbling.
Remove the soup from the heat and stir in the Greek yogurt until the soup is a light orange-red in color. Season with salt and pepper to taste and garnish with fresh parsley, as desired. Enjoy alongside your magical family as they prepare to return to Hogwarts.