For perfectly fried, mozzarella Arancini, dip a rice ball into flour and shake off any excess. Dip floured ball into egg, allowing any excess to drip off. Finish by coating completely in breadcrumbs. Repeat.
Put cooked rice, chicken broth, and 1/2 tsp. salt in a medium saucepan and bring to a simmer over medium heat. Simmer until thickened, 5 to 6 minutes. Stir in parmesan cheese. Remove from heat and let cool. Cut mozzarella into 1/2-inch cubes (you'll have a little left over).
Roll cooled rice into balls the size of golf balls. Push a piece of mozzarella into the middle of each ball, making sure that cheese is completely enclosed. Chill at least 30 minutes or overnight.
Set out 3 plates or shallow bowls. Break eggs into one and beat lightly with a fork. Mix flour with remaining 1/2 tsp. salt and the pepper in another, and put panko in the third bowl.
Fill a 4-qt. pot with enough oil to come 2 in. up side of pot. Insert a deep-fry thermometer and heat oil to 340° over medium-high heat. Dip a rice ball into flour and shake off any excess. Dip floured ball into egg, allowing any excess to drip off. Finish by coating completely in breadcrumbs. Repeat with remaining balls.
Deep-fry rice balls, in batches, until golden brown all over, 2 to 3 minutes, letting temperature return to 340° between batches. With a slotted spoon, transfer to paper towels to drain. Season with salt to taste and serve immediately, with lemon wedges.