In a small saucepan cook the onion in the butter over moderately low heat, stirring, for 5 minutes, stir in 1/4 cup of the flour, and cook the roux mixture over low heat, stirring, for 3 minutes. Stir in the milk and the broth, cook the mixture, stirring, until it forms a paste, and cook the paste, stirring, for 3 minutes. Remove the pan from the heat, stir in the chicken, the sweet potatoes, the cayenne, and salt and black pepper, to taste, and combine the mixture well.
Chill the chicken mixture, covered, for 2 hours, or until it is firm, and roll level tablespoons of it into balls. Dredge the balls in the additional 1/2 cup flour, shaking off the excess, coat them thoroughly with the egg wash, letting the excess drip off, and dredge them in the breadcrumbs, transferring them to wax paper as they are coated. The croquettes may be made up to this point 1 month in advance and kept wrapped well and frozen. Thaw the croquettes for 1 hour. If serving the croquettes immediately, let them dry at room temperature for 1 hour.
In a large saucepan heat 2 inches of the oil until a deep-fat thermometer registers 365 degrees F. Fry the croquettes in batches for 1 to 1 1/2 minutes, or until they are golden brown, and transfer them with a slotted spoon to paper towels to drain. Serve the croquettes with mango chutney, if desired.