Heat 2 tablespoons butter in a medium saucepan over medium heat and add the diced onion. Saute for 2 to 3 minutes until the onion softens and becomes translucent.

Stir in the shredded chicken, chopped olives, parsley, salt, pepper, and 1/4 cup chicken broth. Cook for 3 to 4 minutes, stirring occasionally, until most of the liquid absorbs and the mixture feels thick and cohesive.

Spread the filling on a clean plate to cool completely.

Pour 3 cups chicken broth, 4 tablespoons butter, and 1 teaspoon salt into a medium saucepan and bring to a rolling boil over medium-high heat.

Once boiling, remove from heat and add the 2 cups flour all at once, stirring vigorously with a wooden spoon until a thick, paste-like dough forms. Work it for about 30 seconds until flour is completely incorporated.

Let the dough rest for 2 to 3 minutes until cool enough to handle but still warm.

Once cooled slightly, mix in the egg yolk, stirring vigorously until the dough becomes smooth, shiny, and holds together as one mass.

Place the cooled filling, beaten eggs, and panko breadcrumbs into separate shallow bowls. Have a small bowl of water nearby.

Wet your hands lightly with water and grab about 2 tablespoons of dough, rolling it into a ball. Flatten it gently between your palms into a small disc about 2 inches across.

Place about 1 teaspoon of filling in the center of the dough disc. Fold the dough up and over the filling, sealing the edges by gently pressing them together, then roll between your palms to form a smooth, teardrop shape about 2 inches long.

Place each shaped coxinha on a clean plate or baking sheet. Repeat with remaining dough and filling.

Dip each shaped coxinha into the beaten egg, letting any excess drip off.

Immediately roll the egg-coated coxinha in panko breadcrumbs, pressing gently so they adhere evenly. Place each breaded coxinha on a plate and let the coating dry slightly for 5 to 10 minutes.

Fill a large pot or deep skillet with oil to about 3 inches deep and heat to 350 degrees Fahrenheit using a candy thermometer.

Carefully place 4 to 5 coxinhas into the hot oil, working in batches. Fry for 2 to 3 minutes per side until the coating is deep golden brown and the coxinha floats to the surface.

Transfer fried coxinhas to a plate lined with paper towels to drain excess oil. Serve warm or at room temperature.