Blend the canned tomatoes until smooth. Rinse the can with ½ cup water and add that to the tomatoes before blending.
Heat the olive oil over medium-high heat in a large skillet. Add the guanciale, then reduce heat to medium and cook for 8–10 minutes until golden and the fat has rendered.
Remove the guanciale with a slotted spoon and set aside, leaving the fat in the pan.
Add the garlic (and red pepper flakes if using) and cook for 30 seconds. Add the tomato paste and cook for another 30 seconds. Lower the heat if needed.
Add the white wine and simmer for 1–2 minutes until slightly reduced.
Add the blended tomatoes, salt and pepper. Stir well and simmer over medium-low heat for 10–12 minutes. Add the guanciale back in halfway through.
While the sauce is simmering, cook your pasta until just under al dente, then reserve a cup of pasta water before draining.
Add the pasta to the sauce with ½ cup pasta water and toss well. Let it gently bubble for 2–3 minutes until the sauce coats the pasta.
Turn the heat to low and add the pecorino, tossing continuously until melted and glossy.
Taste and adjust seasoning. Serve with extra pecorino.