Savory cheese turnovers with mint

1 cup grated whole-milk mozzarella cheese (about 4 ounces)
1 cup freshly grated pecorino Sardo or pecorino Romano cheese (about 3 ounces)
1 1/2 tablespoons chopped fresh mint
3 cups unbleached all purpose flour
1 teaspoon salt
7 tablespoons chilled solid vegetable shortening, cut into 1/2-inch pieces
3 tablespoons olive oil
1/2 cup plus 2 tablespoons (about) room-temperature water

1. Mix first 3 ingredients in medium bowl. Cover and let stand at room temperature. Whisk flour and salt in large bowl to blend. Add shortening and rub in with fingertips until coarse meal forms. Add olive oil and 1/2 cup plus 2 tablespoons water, mixing with fork until dough begins to clump together and adding more water by tablespoonfuls if dough is dry. Turn dough out onto work surface and knead briefly until smooth, about 1 minute. Divide in half; roll each half into 1 1/2-inch-diameter log. Wrap logs in plastic and chill 1 hour.
2. Lightly oil baking sheet. Cut each log crosswise into 14 rounds. Roll out each round on floured surface to 3 1/2-inch round. Place 1 heaping tablespoon cheese mixture in center of each of 14 rounds. Brush dough edges lightly with water. Cover each with another dough round. Press edges firmly together, twisting edges of dough a little at a time so that sealed edges resemble thin rope. Place turnovers on prepared sheet, spacing 1 inch apart. (Can be made 6 hours ahead. Cover with plastic wrap and chill.)
3. Preheat oven to 425 F. Bake turnovers until pale golden, about 25 minutes. Place on platter; serve immediately.