Slice the fontina into longwise about ¼-inch thick, then slice the cheese slices into strips about ¼-inch thick. Cut the cheese strips about the length of an olive and set aside.
Take a small piece of cheese and gently stuff it into the olive opening, making sure to keep the olive intact. Repeat with remaining olives and set aside.
In a shallow bowl, beat the egg with a splash of water. In a second shallow bowl, add the cornmeal. With one hand or a fork, roll a few olives at a time in the egg wash then, allowing the excess egg wash to drip off, transfer to the bowl with cornmeal. With your dry hand, roll the olives in the cornmeal until coated then remove and set aside. Repeat with remaining stuffed olives.
Fill a frying pan or dutch oven with a couple of inches of oil and heat over medium-high heat until the oil is shimmering. Test that the oil is hot enough by frying one olive. If the oil is ready, there will be a steady bubbling around the olive. If no bubbling occurs, the oil is not hot enough but if it bubbles too much, then lower the heat and allow the oil to cool down a bit. Fry the olive until golden and crispy, turning it as needed. Using a slotted spoon, remove the olive and transfer to a paper towel or parchment paper lined tray and sprinkle with salt. Repeat with the remaining olives, a small handful at a time.
Serve with a remoulade sauce (recipe below) and enjoy!