In the bowl of a food processor fitted with the bottom blade, add the whole wheat flour, 3/4 cup all-purpose flour, and the salt and pulse 3 to 4 times to combine. Add in the diced cold butter, 1/8 teaspoon cinnamon, and 1/8 teaspoon ginger, and pulse at 3 to 4 second intervals for 6 to 10 times until the mixture resembles sand. Add in the butter milk and pulse until a dough ball forms. Remove from the food processor onto a lightly floured board. Roll the dough into an oval, approximately 16 by 14 inches. Rough edges are okay, but you can trim decoratively if desired. Transfer to a silicone or parchment lined baking sheet.
In a small bowl, combine the remaining 2 tablespoons flour, sugar, and the remaining spices and mix well. Toss this flour mixture with the pears, gently coating. Pile the pear mix in the center of the tart dough, leaving a 3 to 4-inch border, and then fold the edges up and around the pears, leaving an opening in the center. Crimp any breaks in the dough. Place the baking sheet with tart into the refrigerator for 20 minutes.
Preheat the oven to 350 degrees F.
Brush with the melted butter and sprinkle with the turbinado sugar. Place in the oven and bake for 1 hour.
Remove, allow to cool. Serve at room temperature with ice cream or whipped cream.
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