Put the potatoes in a large saucepan with water to cover, and simmer until a knife just pierces the potatoes or they’re about halfway cooked, about 10 to 12 minutes. Drain, cool, peel, and slice ½ inch thick.

Heat a 12-inch nonstick skillet over medium heat, and add the olive oil. When the oil is hot, add the onion, potatoes, and peperoncini, and cook until browned, about 8 to 10 minutes. Season with the salt, and scrape onto a plate.

In a large bowl, toss together the Asiago and polenta. Wipe the skillet clean, and return it to medium heat. Sprinkle half of the cheese mixture in an even layer in the pan, and top with ¾ of the potato mixture, spreading evenly. Make six depressions in the potato mixture, and break an egg into each. Spoon remaining potato mixture gently over each egg. Sprinkle over this the rest of the cheese mixture to cover evenly.

Cook, moving the pan around the flame, so each part of the bottom browns evenly. You will know the frico is ready to flip when it slides in the pan. If necessary, loosen the sides with a knife to help it along. Gently invert the frico into another 12-inch nonstick skillet or slide frico onto a 12-inch plate and invert in same skillet. Continue to cook until the bottom is browned and the eggs are set, about 4 to 5 minutes for yolks that are still runny.