In a bowl, beat eggs with freshly grated cheese before tossing with leftover spaghetti. Make sure the spaghetti is fully covered with the egg. Add a dash or two of salt, to taste, noting that the leftover spaghetti is already seasoned with salt.
Heat the olive oil in a saucepan. To test oil temperature, drop a piece of spaghetti into the pan. If it sizzles upon contact, the oil is ready.
Pour the spaghetti mixture into the pan and flatten it out like a pancake. Fry for 2 minutes on high heat, or until golden brown.
To flip the pasta, cover the pan with a plate larger than the pan, and hold it covered. Flip the pan and plate together to transfer the pasta onto the plate, then slide the uncooked portion back into pan and continue cooking for another 2 minutes, or until golden brown.
Remove the pizza pasta from the pan and place it on a plate lined with a paper towel to absorb the excess oil. Serve warm or cold.