THINLY SLICE GUANCIALE INTO 1-INCH PIECES. PLACE IN A 10-INCH CAST IRON PAN WITH A SPLASH OF OLIVE OIL. COOK ON A LOW FLAME UNTIL THE GUANCIALE IS LIGHTLY BROWNED BUT NOT CRISP. REMOVE WITH A SLOTTED SPOON AND SET ASIDE.
PEEL AND THINLY SLICE THE ONION INTO 1/4-INCH RINGS. ADD TO THE PAN AND TOSS A BIT TO COAT ONIONS WITH THE RENDERED FAT. SALT LIGHTLY. COVER AND CONTINUE TO COOK FOR 30-40 MINUTES, TURNING EVERY TEN MINUTES OR SO, TILL THE CARAMELIZE, TURNING A LIGHT BROWN LIKE, WELL, CARAMEL.
NOTE: IF YOU LIKE, ADD A 1/2 TSP OF CHILI FLAKES.
MEANWHILE, SLICE THE CABBAGE LENGTHWISE IN HALF. CUT OUT THE TOUGH WEDGE FROM THE STEM. SLICE THINLY AS YOU WOULD FOR COLE SLAW.
ONCE THE ONIONS HAVE WILTED AND STARTED TO BROWN, ADD THE SHREDDED CABBAGE.
BRING A POT OF SALTED WATER TO A BOIL. ADD THE PASTA. TOWARDS THE END OF THE COOKING, SCOOP OUT A CUP OF THE PASTA WATER. BOIL PASTA TILL IT IS A LITTLE HARDER THAN AL DENTE. DRAIN.
RETURN THE PASTA, ONIONS, CABBAGE, AND GUANCIALE TO THE PASTA POT OVER A MEDIUM-LOW FLAME. STIR IN 1/2 CUP OF THE PASTA WATER AND 1/2 CUP OF THE GRATED CHEESE. STIR VIGOROUSLY TILL THE SAUCE HAS THICKENED. ADD MORE PASTA WATER IF THE SAUCE IS TOO DRY.
PLACE IN A SERVING BOWL. GARNISH WITH A GENEROUS QUANTITY OF CHOPPED PARSLEY. SERVE WITH A BOWL OF PARMESAN ON THE SIDE.
SERVES 4