Process flours and butter until crumbly. Whisk together 2 eggs, 1 tablespoon of the oil and the water in a small jug until combined. Add to flour mixture; process until mixture almost forms a dough. Knead pastry on a floured surface until smooth.
Roll dough between sheets of floured baking paper into a 1cm (½-inch) thick, 32cm round, large enough to line a 24cm (9½-inch) springform pan. Lift pastry into pan; press over base and three-quarters of the way up the side. Refrigerate 30 minutes.
Preheat oven to 180°C/350°F.
Bring the extra water to the boil in a large saucepan. Add chicken; return to the boil. Reduce heat; simmer, partially covered, for 12 minutes or until chicken is cooked through. Remove chicken; cool 10 minutes then shred coarsely.
Return water to the boil; cook spinach for 1 minute or until wilted. Drain, rinse under cold water; drain. Squeeze out excess water.
Lightly beat remaining eggs in a large bowl. Add spinach, chicken, garlic, rice, fetta, ricotta, green onion and parsley; stir to combine. Fill pastry case with chicken filling.
Bake pie for 50 minutes or until pie is cooked through and pastry is golden.