Heat oil in a deep fryer or heavy-bottomed saucepan to 350°F (175°C). Use a thermometer for accuracy, ensuring a safe and consistent temperature for frying.

Place ½ inch of water in a saucepan and bring to a boil. Carefully add the six cold eggs, cover with a lid, and reduce heat to medium-high. Cook for approximately 6 minutes to achieve soft-boiled centers. Immediately transfer the eggs to cold running water to halt cooking. Peel and pat them dry with paper towels.

In a large bowl, combine the Italian sausage with the dry mustard, nutmeg, and cayenne pepper. Mix thoroughly and divide into six equal portions.

Place a piece of plastic wrap on a clean, flat surface. Flatten one portion of sausage into an oval approximately ⅛-inch thick. Place one peeled egg in the center. Using the plastic wrap to assist, gently mold the sausage around the egg until fully enclosed. Seal all edges firmly. Repeat with remaining eggs and sausage portions.

Place the flour in one shallow bowl, the two beaten eggs in a second, and the panko bread crumbs in a third.

Carefully dredge each sausage-wrapped egg in flour, ensuring full coverage. Dip into the beaten eggs, then coat thoroughly with panko bread crumbs. Lightly press to adhere and shake off any excess.

Fry the breaded eggs in batches for 5–6 minutes, turning occasionally to ensure even browning. Once golden and crisp, remove with a slotted spoon and place on a wire rack to cool for 5 minutes before serving.