Soak potatoes in a large bowl of cold water for 30 minutes.
Preheat oven to 450°F with rack in center position.
Squeeze potatoes dry in a clean kitchen towel to remove as much liquid as possible.
Place a 10-inch cast-iron skillet on center oven rack.
Toss together squeezed potatoes, Halloumi, flour, oregano, lemon zest, salt, and pepper in a large bowl until evenly distributed.
Stir in water until mixture forms a shaggy, thick batter.
Remove skillet from oven, and add 2 tablespoons oil; carefully swirl to coat.
Add potato mixture, and spread into an even layer, pressing lightly with a fork or spatula.
Drizzle evenly with remaining 1 tablespoon oil.
Return skillet to oven, and bake until pancake is golden brown on top and deeply browned around edges, 35 to 45 minutes.
Let cool in skillet 5 minutes.
Garnish with oregano, lemon zest, pepper, and flaky sea salt.
Cut into 6 wedges, and serve.
