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1/2 pound small Yukon Gold potatoes
6 tablespoons extra-virgin olive oil, divided
1 tablespoon plus 2 teaspoons finely chopped oregano, divided
2 1/4 teaspoons fine sea salt, divided
8 (5-ounce) pieces skinless black cod, Pacific cod, or haddock fillet (about 1 inch thick), any bones removed
1 lemon, very thinly sliced
6 garlic cloves, thinly sliced
1/2 cup Kalamata-style black olives, pitted and cut into slivers
1/2 cup flat-leaf parsley leaves
an adjustable-blade slicer; 8 (12- to 15-inch) squares of parchment paper; kitchen string.
Preheat oven to 400°F with a baking sheet on bottom rack.
Cut potatoes into very thin slices with slicer. Toss potatoes with 2 tablespoons oil, 1 teaspoon oregano, and 1/4 teaspoon sea salt. Divide potatoes among parchment squares, arranging them in center, slightly overlapping, then top with a piece of fish. Sprinkle each fillet with a scant 1/4 teaspoon sea salt, then top each with a lemon slice, a few garlic slices and olive slivers, parsley leaves, 1/2 teaspoon oregano, and 1/2 tablespoon oil.
Gather sides of parchment up over fish to form a pouch, leaving no openings, and tie tightly with kitchen string. Put packages on hot baking sheet and bake until fish is just cooked through, 15 to 22 minutes.