Preheat oven to 375°F
Toss pear slices, 1 teaspoon all-purpose flour, 1 tablespoon sugar, cinnamon, nutmeg and salt in a medium bowl.
Whisk 1/3 cup all-purpose flour, whole-wheat flour and the remaining 1 tablespoon sugar in a medium bowl. Cut in butter with a pastry cutter or a fork until the mixture resembles coarse meal. Sprinkle oil over the mixture and stir with a fork until evenly combined. Add 1 tablespoon water and stir until the dough just stays together when pressed with a fork; add up to 1 additional tablespoon of water if the dough seems too dry.
Line a work surface with parchment paper or a silicone baking mat, generously dust with flour and turn the dough out onto it. Form the dough into a small patty, dust the top with flour and roll into a rustic 10-inch circle, adding more flour if necessary to prevent sticking. Transfer the crust to a baking sheet with parchment paper or baking mat in place.
Lay the pear slices in decorative, overlapping circles on top of the crust, leaving a 1-inch border around the edge. Spoon any remaining pear juice over the slices. Pick up the edges of the crust using a spatula and fold over the pears. The crust will not meet in the center.
Bake the tart until lightly browned and bubbling, about 40 minutes. Cool for 10 minutes before serving.