Potatoes:
1/4 cup extra-virgin olive oil
1 pound small potatoes, such as ruby crescents, cut into 1/8-inch thick rounds
1 medium onion, quartered lengthwise, and cut crosswise into 1/4-inch-thick slices
2 teaspoons chopped fresh rosemary
2 teaspoons chopped fresh thyme
Coarse salt and freshly ground white pepper

Snapper:
1/2 cup extra-virgin olive oil, plus more as needed
20 cloves roasted garlic
1 sprig fresh rosemary
4 (7-ounce) skin-on red snapper fillets
Coarse salt and freshly ground white pepper
3/4 cup dry white wine
2 cups clam broth, plus more as needed
2 ripe tomatoes, peeled, seeded and cut into 1/4-inch dice
16 Kalamata olives, pitted and coarsely chopped (about 1/3 cup)
2 tablespoons roughly chopped fresh flat-leaf parsley
8 thin-sliced rounds lemon

Preheat the oven to 400 degrees F.

Make the potatoes: Heat the oil in an ovenproof 12-inch non-stick skillet over medium-low heat. Add the potatoes and cook, stirring, until soft, about 10 minutes. (The potatoes shouldn't brown.) Add the onion, rosemary, and thyme, and season with salt and pepper. Cook, covered, until the onions soften, about 5 minutes. Transfer the potatoes to bowl and set aside. (The potatoes may be made up to 3 days in advance and refrigerated.)

Make the snapper: Heat the oil in the ovenproof skillet over medium heat. Arrange the potatoes in 4 thick mounds in the skillet and scatter the garlic and rosemary around them.

Season the snapper with salt and pepper. Place 1 fillet on top of each mound. Add the wine, bring to a boil, and cook until reduced by half, about 2 minutes. Pour in the clam broth. Bring to a boil, cover, and braise in the oven until the snapper is barely opaque in the center, about 7 to 8 minutes.

Using a slotted spatula, transfer the potato mounds topped with the snapper to the center of 4 warmed dinner plates. Return the skillet to high heat and boil until lightly thickened, about 2 minutes. Add the tomatoes, olives and parsley and cook for 15 seconds. Taste for balance, adding some olive oil or more clam broth, if desired. Season with salt and pepper. Spoon half the sauce over the fish fillets and pour the rest into a warmed sauce boat. Serve immediately, garnished with the lemon slices, with the sauce passed on the side.