Cut 1/3 off the top of each mozzarella ball. Scoop out some of the cheese with a teaspoon to make a hole in each ball. Stuff hole with 1 teaspoon basil and 1 teaspoon sun-dried tomatoes; cover with the top.
Beat eggs using a fork in a shallow bowl. Pour panko bread crumbs, salt, and pepper into a second shallow bowl.
Dip mozzarella balls into beaten eggs, holding them with 2 forks so the top doesn't fall off. Dip in bread crumbs, turning gently to coat.
Heat oil in a large saucepan to about 375 degrees F (190 degrees C). Test if oil is hot by dropping a few bread crumbs into the oil. If the oil fizzles, it is hot enough. Drop mozzarella balls carefully into the hot oil and fry on both sides until nicely browned and crispy, about 2 minutes per side. Remove from oil with a slotted spoon and drain on paper towels.
We have determined the nutritional value of oil for frying based on a retention value of 10% after cooking. Amount will vary depending on cooking time and temperature, ingredient density, and specific type of oil used.
Per Serving: 494 calories;32.7 g fat;
22.6 g carbohydrates;
33.6 g protein;
166 mg cholesterol;
914 mg sodium.