Bring a pot of water to a boil and then add chicken breasts. Cover, turn the heat down to low-medium, and simmer for about 20-30 minutes (depending on the sizand no longer pink inside.
Meanwhile, add butter, chicken stock, salt, nutmeg, and milk to another pot and bring to a simmer. Add flour in batches, stirring, until combined. Let cool.
Once chicken is done, shred it with a meat shredder and place it in a large bowl. Add the remaining filling ingredients and mix together.
Roll dough into small balls and use your thumbs to flatten into circles. Add some filling in the middle and bring up the edges of the circle, pinching together at the top.
Place eggs and panko in separate bowls. Dip each coxinha first into the eggs and then into the panko.
Place a large pan on medium-high heat with about ½ inch of vegetable oil. Working in batches, fry coxinhas until golden on all sides. Set aside to dry and serve warm, with a side of salsa.