1. In a 9- or 10-inch skillet, combine
the onion, the olive oil and the hot pepper and cook over medium
heat until the onion is lightly golden, about 6 minutes.
2. Add the tomato puree, dried marjoram,
and a big pinch of salt to start. Simmer for 5 or 6 minutes, until
the sauce has concentrated a little. You can set the pan aside now
(at room temperature or in the refrigerator) if you are not cooking
the eggs until later.
3. Before cooking the eggs, bring the sauce
back to a simmer, taste and add more salt if necessary, then break
the eggs into the bubbling sauce. Cover and cook until the eggs
are done to taste, meaning with fully set whites and runny yolks,
or until the yolks are set further or completely.
4. Serve with grated Parmigiano-Reggiano,
pecorino, or ricotta salata.