Put a baking sheet in the oven and preheat to 500 degrees F. Toss the potatoes with 2 tablespoons olive oil, 1/2 teaspoon salt, a few grinds of pepper and 1 grated garlic clove. Spread out on the baking sheet and roast until browned and tender, 20 to 25 minutes.
Meanwhile, heat the remaining 2 tablespoons olive oil in a large skillet over medium-high heat. Add the sausage and cook, stirring, until browned, 6 to 8 minutes; remove to a plate with a slotted spoon. Add the onion and bell pepper to the skillet; cook, stirring, until lightly browned, 5 to 7 minutes. Add the remaining garlic and the cherry peppers; cook until softened, about 1 minute. Add the cherry pepper brine and wine and cook, scraping up any browned bits, until the liquid is mostly reduced, 1 minute. Add the chicken broth, rosemary and a pinch of salt; bring to a simmer.
Season the snapper with salt and pepper. Arrange skin-side up on top of the vegetables in the skillet. Scatter the sausage around the fish. Adjust the heat to maintain a gentle simmer, cover and cook until the fish is just cooked through, 5 to 6 minutes.
Divide the sausage, vegetables and snapper among plates; discard the rosemary. Serve with the potatoes. Sprinkle with parsley.