1. Preheat oven to 400°.
2. Lightly spoon 1.1 ounces (about 1/4 cup) all-purpose flour into a dry measuring cup; level with a knife. Combine 1.1 ounces all-purpose flour, ice water, vinegar, and almond extract in a small bowl; stir with a fork until well blended to form a slurry.
3. Combine remaining 5.1 ounces (about 1 cup plus 2 tablespoons) all-purpose flour, 2 tablespoons sugar, almond flour, and salt, stirring with a whisk. Cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Add slurry; stir just until moist. Turn dough out onto a lightly floured surface; knead lightly 5 times. Gently press dough into a 4-inch circle on heavy-duty plastic wrap. Cover with additional plastic wrap. Carefully roll dough into a 14-inch circle; freeze for 10 minutes.
4. Remove dough from freezer; remove top sheet of plastic wrap. Let stand 1 minute or until pliable. Place dough, plastic wrap side up, onto a baking sheet lined with parchment paper; remove remaining plastic wrap.
5. Combine cornstarch and 2 tablespoons sugar; sprinkle over dough, leaving a 2-inch border. Arrange apricots spokelike on top of cornstarch mixture, leaving a 2-inch border. Fold edges of dough over apricots (dough will only partially cover apricots).
6. Combine jam and honey in a small microwave-safe bowl; microwave on HIGH 45 seconds. Brush jam mixture over apricots and dough edges. Sprinkle with remaining sugar. Bake at 400° for 35 minutes or until crust browns. Remove from oven; sprinkle with thyme. Cool 10 minutes.