Heat 1/4 cup of the olive oil in a large deep skillet with a lid over medium heat. Place the potatoes in the pan cut-side down. Add the garlic and cook until the potatoes are slightly golden and crisp, 4 to 5 minutes. Add the escarole, season with salt and pepper, then add about 1/3 cup water. Cover and steam until the escarole wilts, about 5 minutes.
Season the fish with salt and pepper; place on top of the greens in the pan and sprinkle with the oregano leaves. Cover and steam until the fish is just cooked through, about 5 more minutes.
Meanwhile, whisk the lemon juice in a bowl with the remaining 1/4 cup olive oil; season with 1 teaspoon salt and plenty of pepper.
Carefully lift the fish off the greens and transfer to rimmed plates or bowls. Distribute the greens, potatoes and pan juices around the fish. Drizzle with the lemon-pepper oil.