Preheat oven to 400°.
To prepare dough, lightly spoon 2 1/4 cups flour into dry measuring cups; level with a knife. Place 2 1/4 cups flour, granulated sugar, and salt in a food processor; pulse to combine. Add all but 1 teaspoon butter; pulse 10 times or until mixture resembles coarse meal. Combine ice water and vinegar. With processor on, slowly add ice water mixture through food chute, processing just until combined (do not form a ball). Press mixture gently into a 6-inch circle on plastic wrap. Cover and chill for 30 minutes.
To prepare filling, combine Poached Quinces, cognac, vanilla, and apples in a large bowl. Sprinkle with 1 tablespoon flour; toss well to combine.
Remove dough from the refrigerator. Slightly overlap 2 sheets of plastic wrap on a slightly damp surface. Unwrap and place chilled dough on plastic wrap. Cover dough with 2 additional sheets of overlapping plastic wrap. Roll dough, still covered, into a 14-inch circle. Remove top sheets of plastic wrap; place dough, plastic wrap side up, on a baking sheet lined with parchment paper.
Remove plastic wrap. Spoon filling into center of dough, leaving a 2-inch border. Fold edges of dough toward center, pressing gently to seal (dough will only partially cover filling). Lightly coat dough with cooking spray. Sprinkle turbinado sugar over dough; dot filling evenly with remaining 1 teaspoon butter. Bake at 400° for 30 minutes or until crust is golden brown.