In a large bowl, whisk together the flours, sugar, salt, and flax seeds. Cut in the butter with your hands and/or a fork, rubbing and whisking the butter into the flours until it resembles a coarse meal. Stir in the buttermilk all at once, and stir until combined. Gather the mixture into a ball; you may add a bit more buttermilk if it is too dry and hard to hold together. Divide in half, wrap in plastic wrap, press into a 9-inch round, and then refrigerate the pastry rounds for at least 30 minutes.

Transfer 1 dough round to a 9-inch deep-dish pie dish and gently press into the dish. Trim the edges flush with the rim. Refrigerate the pie shell for 30 minutes. Keep the rest of the dough in the fridge until ready to use.

In a large Dutch oven or cast iron pan over medium heat, stir together the apples, honey, cinnamon, ginger and lemon juice. Cover and cook, stirring occasionally, until the apples are just tender, about 20 minutes. Uncover and let cool to room temperature. Stir in the cornstarch.

In a heavy 4-quart saucepan over medium heat, combine the brown sugar, maple syrup, butter and salt. Cook until the mixture is bubbling vigorously, about 9 minutes, stirring only during the first 2 to 3 minutes of cooking. Off the heat, carefully stir in 1/4 cup of the cream, then stir in the remaining 1/4 cup cream. Let cool until just warm.

Heat an oven to 400°F.

Let the pie shell, cutouts and dough round stand at room temperature for 5 minutes. In a large bowl, combine the apple mixture and 3/4 cup of the caramel; reserve the remaining caramel for serving. Pour the apple filling into the pie shell and place the top crust over the pie. Trim the edges flush with the rim and press the top and bottom crusts together.