In a large shallow dish, whisk together the milk, eggs, granulated sugar, lemon zest, ground nutmeg, and coarse salt. Cut the pitas in half crosswise and place in dish. Soak 15 minutes, flip halfway through.

In a large nonstick skillet, melt the unsalted butter over medium until foaming. Lift 4 pita halves from eggmixture, letting excess drip off, and cook until golden brown on both sides, about 12 minutes, flipping halfway through. Transfer to a plate and cover with foil to keep warm; repeat with remaining pita halves. Cut into wedges and dust with confectioners' sugar.