Finely crush the peppermint and cumin using a mortar, mix with the flour and salt in a bowl. Add the water and oil, knead to form a soft, smooth dough. Shape the dough into a ball, cover and leave to rest at room temperature for approx. 1 hr.
Mix the spinach, feta, oil and garlic, season.
Divide the dough into 10 portions, sprinkle a little flour on the work surface and roll out into circles approx. 1 mm thick. Spoon the filling onto one side of each circle. Brush the edges with a little water, fold the circles together into half-moon shapes. Firmly press down the edges, roll over them with the rolling pin.
Grill the gözleme, with the lid down, for approx. 3 mins. on each side over/on a medium heat (approx. 200 °C, wrap in foil and keep warm.