Place the cubed potatoes in a large pot and cover with cold water by about 2 inches. Bring to a boil over high heat and cook for about 8 to 10 minutes until the potatoes are fork-tender and break apart easily.

Pour the potatoes into a colander and let all the water drain completely. Pass the hot potatoes through a potato ricer into a large mixing bowl, or mash them thoroughly with a potato masher until smooth and lump-free.

While the potatoes are still hot, add the chicken broth, butter, flour, and egg yolk to the bowl. Mix everything together with a wooden spoon or your hands until a soft dough forms, then season with salt and pepper.

Spread the dough on a plate or baking sheet and refrigerate for at least 15 minutes until it's cool enough to handle.

Heat 2 tablespoons of butter in a medium saucepan over medium heat and add the diced onion. Saute for about 3 minutes until the onion is soft and starting to turn translucent, then add the garlic and cook for another 30 seconds until fragrant.

Add the shredded chicken, tomato paste, chicken broth, parsley, salt, and pepper to the pan with the onion and garlic. Stir well and simmer for about 5 minutes until the filling is thick and most of the liquid has reduced. Let cool.

Spread some flour on a work surface to prevent sticking. Wet your hands slightly, take about 2 tablespoons of dough, and flatten it into a small disc in your palm.

Place about 1 teaspoon of the cooled filling in the center of the dough disc. Gently fold the edges up around the filling and pinch them together at the top to form a closed teardrop or cone shape, then smooth the seams with damp fingers. Repeat with remaining dough and filling.

Place the flour in one shallow bowl, the beaten eggs in another, and the panko breadcrumbs in a third. Line up these bowls in order from left to right for efficient breading.

Working with one coxinha at a time, roll it lightly in flour, then dip it into the beaten egg, allowing excess to drip off. Finally, roll it in panko breadcrumbs until completely covered, pressing gently so the coating adheres.

Fill your deep pot with oil to a depth of about 3 to 4 inches and heat it to 350 degrees Fahrenheit, using a thermometer to check the temperature.

Once the oil reaches the target temperature, carefully slide 3 to 4 coxinhas into the hot oil. Fry for about 2 to 3 minutes, turning them occasionally with a slotted spoon, until the coating is deep golden brown all over.

Remove them with the slotted spoon and place on a paper towel-lined plate to drain excess oil. Repeat with remaining coxinhas.

Allow the coxinhas to cool for about 2 to 3 minutes before eating. Serve warm with your choice of dipping sauces.