How to Make It
Prepare the caramel: Cook 1/2 cup granulated sugar, 3 tablespoons water, and corn syrup in a small saucepan over medium-high, stirring constantly with a whisk just until sugar dissolves, about 1 minute. Bring to a boil. Boil until mixture is a deep amber color, 7 to 9 minutes, gently swirling pan occasionally and brushing sides with a wet pastry brush as needed to wash any crystals from side of pan. Remove from heat; slowly stir in evaporated milk. Stir in miso. Cool 10 minutes. Transfer caramel to a blender; blend until smooth. Let stand at room temperature.
Prepare the crust: Combine 25 ounces all-purpose flour, oat flour, baking powder, and 1/4 teaspoon salt in a large bowl. Add shortening and 1 tablespoon butter pieces; combine, using your fingers, until shortening and butter are well distributed and small clumps begin to form. Stir in 1 tablespoon water. Add up to 3 additional tablespoons water, 1 teaspoon at a time, stirring just until dough begins to come together. Turn dough out on a lightly floured surface; gently knead 1 to 2 times. Shape into a ball; flatten into a disk, and wrap tightly in plastic wrap. Chill 20 minutes. Unwrap dough, and transfer to floured work surface. Roll to an 11-inch circle; fit into a 9-inch pie plate. Fold edges under; crimp. Freeze 45 minutes (or up to 2 months).
Prepare the topping: Whisk together oats, pecans, 2 tablespoons brown sugar, 2 tablespoons all-purpose flour, and 1/4 teaspoon salt in a medium bowl. Sprinkle with 1/4 cup butter pieces. Combine, using your fingers, until small clumps begin to form. Chill until ready to use.
Preheat oven to 425°F.
Prepare the filling: Bring 8 cups water to a boil in a large saucepan. Place apples in a large bowl. Pour boiling water over apples; let stand 10 minutes. Drain well; pat dry. Return apples to bowl. Add 1/4 cup brown sugar, 1 tablespoon tapioca flour, and cinnamon; toss to coat. Whisk together 2% milk, vinegar, 1/4 teaspoon salt, and remaining 1 tablespoon tapioca flour. Pour over apples; toss to combine.
Remove crust from freezer. Spread filling evenly in crust. Sprinkle evenly with topping. Bake at 425°F for 12 minutes; reduce oven temperature to 375°F. Place a foil-lined baking sheet on rack below pie to catch drippings. Loosely cover pie with foil to prevent overbrowning. Bake until done, 35 to 40 minutes, rotating pie halfway (on same rack) after 20 minutes. Cool on a wire rack 15 minutes.
Heat caramel in a saucepan over medium-low until warm, stirring constantly. Drizzle over pie; serve warm.
Note: We recommend seeking out Earth Balance shortening because, unlike most other shortenings, it contains no trans fats.