To begin, cook the chicken breasts in lightly salted water for about 15-20 minutes, or until fully cooked. Save 2 cups of the chicken broth for later use. Once the chicken is cooked and cooled slightly, shred it finely and set aside.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and garlic, and sauté until golden and fragrant, about 3-4 minutes. Add the shredded chicken, stirring well to incorporate the flavors. Season with salt and pepper, then mix in the cream cheese and fresh parsley. Cook for another 2-3 minutes, then remove from heat and set aside to cool.
To make the dough, bring the reserved 2 cups of chicken broth, butter, and salt to a boil in a saucepan. Once the broth is boiling, reduce the heat to low and slowly add the flour, stirring continuously. Keep mixing until the dough forms a ball and pulls away from the sides of the pan. This process should take about 5-7 minutes.
Remove the dough from the heat and allow it to cool slightly. Knead the dough on a lightly floured surface until smooth and elastic. This step ensures that the dough becomes soft and easy to handle.
Take small portions of the dough and flatten them into disks in your hand. Place a spoonful of the chicken filling in the centre of the dough disk. Carefully fold the dough around the filling, shaping it into a teardrop or drumstick shape. Make sure the edges are sealed completely to avoid the filling leaking during frying.
Once all the coxinhas are shaped, set up a breading station. In one bowl, place the beaten eggs, and in another bowl, place the breadcrumbs. Dip each coxinha in the beaten egg, then roll it in the breadcrumbs, ensuring they are well coated.
Heat vegetable oil in a deep fryer or large pot to 350°F (175°C). Fry the coxinhas in small batches, turning occasionally, until golden brown and crispy on all sides—this should take about 4-5 minutes per batch. Be careful not to overcrowd the pan, as it will lower the oil temperature and affect the crispiness.
Drain the fried coxinhas on a paper towel-lined plate to remove excess oil. Serve them hot, accompanied by your favourite dipping sauce, such as spicy chili sauce or Brazilian vinaigrette, to enhance the flavors. The crispy exterior contrasts beautifully with the creamy, savoury chicken filling inside.