You smell this one before you see it. I've been halfway across a fairground, headed somewhere else on purpose, and that mix of sausage fat, peppers, and onions cooking down has turned me around without a single thought in between. Wallet out. Plans changed. That's fair food doing its job.
At home I make it the same way and I don't dress it up. Good Italian sausage, half hot and half sweet so nobody gets bored and nobody cries at the table. Peppers sliced thick so they hold up in the pan. Onions sliced thick too, because thin onions vanish and I want to taste them after they go sweet.
Two things matter here and both are about patience. The sausage needs real color before it leaves the pan. The peppers and onions need time on low heat until they slump and get sweet at the edges. Rush either one and you get a pan of almost. Give them the time and the juices in the pan turn into the sauce on their own. Cooked is cooked, and this one announces itself from the next room.
Set a large heavy skillet or Dutch oven over medium heat and add 1 tbsp of the olive oil. Add the sausage links in one layer and cook for 8 to 10 minutes, turning every couple of minutes, until they're browned on most sides. They don't have to cook through yet. Lift them out onto a plate and leave the fat in the pan.
Add the rest of the olive oil to the same pan. Add the peppers and the onions with the kosher salt and toss them in the fat. Turn the heat down to medium low. Cook for 18 to 20 minutes, stirring every few minutes, until the onions turn soft and sweet and the peppers slump. If the pan looks dry, add a spoonful of water and keep going.
While the vegetables cook, slice the sausage links on a bias into 1 inch pieces. You'll lose a little juice on the board. Tip the board over the pan later and pour that juice back in. Waste nothing.
Push the peppers and onions to the edges of the pan. Add the garlic, the oregano, and the red pepper flakes to the middle and cook for 30 seconds, stirring the whole time, until the garlic smells strong. Don't walk away here. Garlic goes from fine to bitter fast.
Pour in the broth and scrape the bottom of the pan with a wooden spoon until every browned bit lifts off. Those bits are flavor you already paid for in time. Let the liquid bubble for 1 minute.
Slide the sausage pieces and any juice from the board back into the pan and stir everything together. Cover the pan, turn the heat to low, and simmer for 8 to 10 minutes, until the sausage is cooked through and registers 160°F on a thermometer. Uncover the pan for the last 2 minutes so the juices tighten up a bit.
Stir in the red wine vinegar. Taste a pepper and a piece of sausage together. Add salt if it tastes flat and more red pepper flakes if you want more heat. Turn the heat off and let the pan sit for 2 minutes.
Toast the split rolls cut side down in a dry skillet or under the broiler until the edges turn crisp. If you're using provolone, lay a slice on the bottom half of each warm roll. Pile the sausage and peppers on top with plenty of the pan juices, close the rolls, and serve right away with napkins close. You'll need them.
Slice your peppers and onions thick, about 1/2 inch. Thin strips cook down to mush before the sausage finishes, and you lose the bite that makes each mouthful different. Thick cuts go soft and sweet and still hold their shape in the roll. If a roll starts to fall apart halfway through, flip it over and eat it upside down. The top holds better than the bottom once the juices hit.
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