Slice the chicken breasts into small, even pieces about 2 cm (¾ inch) thick. Pat them dry with paper towels to remove excess moisture, which helps the coating stick better.
In a mixing bowl, whisk the eggs with a pinch of salt and a splash of water until well combined. This will create a smooth, slightly frothy egg wash that helps the breadcrumbs adhere.
In another bowl, combine the panko breadcrumbs with smoked paprika, salt, and black pepper. Mix thoroughly to evenly distribute the smoky flavor throughout the coating.
Dip each chicken piece into the egg wash, allowing any excess to drip off, then transfer it to the breadcrumb mixture. Press lightly to ensure the coating sticks evenly all around the chicken.
Heat the vegetable oil in a deep-fryer or heavy-bottomed pot to 180°C (350°F). Use a thermometer to maintain a steady temperature for crispy, evenly cooked nuggets.
Carefully lower a batch of coated chicken pieces into the hot oil using a slotted spoon. Fry for 4–5 minutes, turning occasionally, until golden brown and crispy on all sides.
Once golden and cooked through (internal temperature should reach 75°C or 165°F), lift the nuggets out with a slotted spoon and transfer to a wire rack to drain excess oil. Repeat with remaining chicken pieces.
Allow the nuggets to rest for 2 minutes to set the crispy coating. Serve immediately, hot and crunchy, with your favorite dips or sides.