1 In a food processor, combine whole-wheat flour, 250 grams (approximately 1 cup) pastry flour, 30 grams (approximately 1/4 cup) granulated sugar and 1 generous pinch of salt and pulse to combine.
2 Cut butter into small pieces and place in food processor. Pulse to combine.
3 Add vinegar and 10-12 tablespoons ice-cold water and process to a smooth dough as quickly as possible.
4 Divide dough into 2 equal portions, wrap each in plastic wrap and let rest for about 2 hours in the refrigerator. (The dough can be made up to 2 days in advance.)
5 Rinse lemon in hot water and wipe dry. Finely grate 1 teaspoon lemon zest and squeeze 1 tablespoon lemon juice. Mix 70 grams (approximately 1/4 cup) granulated sugar, the brown sugar, remaining flour, lemon zest and juice and cinnamon in a bowl.
6 Peel apples, cut into quarters, remove seeds and cut into very thin slices.
7 Add apples to brown-sugar mixture in bowl and toss to combine well.
8 Roll out dough on a floured surface into 2 rounds, each about 30 cm (approximately 12 inches) in diameter.
9 Press 1 dough round into bottom and up side of tart pan (or springform pan).
10 Pour apple filling into tart pan. With a pizza cutter, cut other dough round into strips, about 2 cm (approximately 3/4 inch) wide.
11 Weave dough strips over filling, pressing firmly on edges.
12 Brush dough with milk and lightly sprinkle with remaining sugar. Bake on second rack from bottom of preheated oven at 180°C (fan 160°C, gas: mark 2-3) (approximately 350°F) until crust is golden brown and filling is bubbling, about 70 minutes. Let pie cool on a cooling rack and serve warm or at room temperature.