Put the oil, butter, and onion in a saucepan and turn on the heat to medium. Sauté the onion until it becomes colored a pale gold, then add the guanciale. Cook for about 1 minute, stirring once or twice. Add the tomatoes, simmer for 25 min. Taste and correct for salt and hot pepper.
Toss the pasta with sauce, then add both cheeses, and toss thoroughly again.
Recommended pasta, it’s impossible to say “all’Amatriciana” without thinking
“bucatini”. But the penne or rigatoni are the second option.