A photo like it (a Primanti Bros. sandwich) · rrafson (CC BY-SA 3.0) via Wikimedia Commons · source
Chef's home version of the Primanti Bros. sandwich: grilled capicola and provolone on thick soft Italian bread, with a sweet-sour vinegar slaw, tomato and hot fries stacked inside the sandwich, not beside it.
300 g (10 oz) capicola (or pastrami), thinly sliced
8 slices provolone
2 ripe tomatoes, sliced
For the slaw: 1/2 small green cabbage (about 400 g / 14 oz), finely shredded, 4 tbsp cider or white vinegar, 2 tbsp neutral oil, 1 1/2 tbsp sugar, 1/2 tsp celery seed, 1 tsp salt, black pepper
For the fries: 3 large russet potatoes (about 750 g / 1 2/3 lb), neutral oil for frying, salt
How to make it
Make the slaw (5 min, then rest): Whisk the vinegar, oil, sugar, celery seed, salt and pepper until the sugar dissolves, toss with the cabbage and leave at least 20 minutes. No mayo: it should be sharp and wet.
Cut and soak the potatoes (10 min): Cut the potatoes into 1 cm (3/8 in) fries, rinse in cold water until it runs clear, then dry very well on a towel.
Fry twice (15 min): Heat 5 cm (2 in) oil to 160 C (325 F) and fry the potatoes in batches 5 minutes until soft but pale; drain. Raise the oil to 190 C (375 F) and fry again 2 to 3 minutes until golden and crisp. Drain and salt at once.
Grill the meat (3 min): In a hot skillet, sear the capicola 30 seconds a side, pile it into 4 mounds, lay 2 slices of provolone on each, add a splash of water and cover 1 minute to melt.
Stack (2 min): On a slice of bread put the meat and cheese, then a big handful of hot fries, a pile of drained slaw and 2 tomato slices. Top with the second slice, press down and cut in half. Eat at once, while the fries are hot.
Tips
Use oven fries if you'd rather not deep-fry; make them extra crisp, because the slaw softens them.
The bread should be soft and thick, not crusty: it has to hold everything together.