Wash the sweetbreads and soak them in ice water for 1 hour.

Drain the sweetbreads.

Cover the sweetbreads with water.

Add 2 teaspoons of vinegar or lemon juice and about 1 teaspoon of salt.

Bring to a boil and cook over low heat 15 minutes.

Drain, cover with cold water and let cool.

Drain and remove the membranes, tubes, and connective tissues from the sweetbreads.

Dice the parboiled sweetbreads.

Melt the butter in a saucepan.

Stir in the onion and half the flour.

Add the broth and cream, stirring steadily to the boiling point.

Cook over low heat 10 minutes, stirring occasionally.

Stir in 1 1/2 teaspoons of the salt and the cayenne pepper.

Cool 10 minutes.

Fold in the sweet breads, shallots or green onions, and parsley.

Chill the mixture thoroughly.

Form the chilled mixture into 12 croquettes.

Beat together the eggs, milk, and remaining salt.

Dip the croquettes in the remaining flour.

Dip the flour-coated croquettes in the beaten eggs.

Dip the egg-coated croquettes in the bread crumbs, coating them thoroughly.

Heat the oil to 390 F.

Fry a few croquettes at a time until browned.

Drain the fried croquettes.

Place the drained croquettes on a hot platter.

Garnish with parsley sprigs.

Serve the croquettes immediately.