In a saucepan, melt the butter and sauté the onion and garlic until soft and translucent.Add the flour and whisk until smooth. Cook for a few minutes until the mixture starts to turn golden.Gradually whisk in the milk and continue to cook, stirring constantly, until the mixture thickens and forms a smooth, creamy sauce.Add the shredded chicken, parsley, salt, and pepper, and stir to combine. Remove from heat and let cool.Once the chicken mixture has cooled, shape it into small croquettes.Dip each croquette into the beaten eggs, then coat it with breadcrumbs.A deep frying pan with medium heat is used to heat the oil. Fry the croquettes in batches until golden brown on all sides, about 3-4 minutes per batch.Drain the croquettes on paper towels to remove excess oil.Serve hot with your favorite dipping sauce.