Cut the feta into 3-inch / 7.5-cm squares about 1/2 inch / 1.5-cm thick.

On a large flat plate, toss the pistachios, the mastiha, and the ground black peppercorns. Dip the feta pieces on both sides in the egg, let the runoff drip off, and then press each piece of feta on both sides into the pistachio mixture. Place on a sheet pan or tray lined with wax or parchment paper, cover in plastic wrap and freeze for 30 minutes or up to a few hours.

Heat the olive oil and butter in a large, heavy nonstick frying pan. Sauté the feta pieces one or two at a time over medium heat, until the pistachio crust begins to brown lightly. Flip carefully with a spatula to sauté on the other side. Remove from the pan and serve hot. Repeat with the remaining pieces.