Apple Pie Coffee Cake

2 large eggs
1 tablespoon vegetable oil
1/4 teaspoon pure vanilla extract
3/4 cup sugar
1 cup unbleached all-purpose flour
2 teaspoons baking powder
1/2 teaspoon ground cinnamon
1/4 teaspoon ground allspice or nutmeg
1/4 teaspoon salt
2 cups peeled, cored, and thinly sliced firm tart
    apples (about 1 1/2 pounds)
1 tablespoon turbinado (raw) sugar, for sprinkling on top

Heat the oven to 375 degrees F (350 degrees if using a Pyrex or dark-finish pie plate). Grease a 10-inch pie plate.

In a medium bowl, combine the eggs, oil, vanilla extract and sugar, beating with a wooden spoon until thick, about 1 minute. Add the flour, baking powder, cinnamon, allspice, nutmeg, and salt. Beat vigorously until the batter has a crumbly consistency, about 1 minute. Fold in the apples and mix until the apples are evenly coated and the batter becomes moist and smooth. The batter will be fairly stiff.

Scrape the batter into the prepared pan and smooth into an even layer with a metal spatula. Sprinkle the top evenly with the sugar. Bake on the center rack of the oven 30 to 35 minutes, until the center is firm when gently pressed. A cake tester inserted into the center should come out clean, the top and bottom of the cake should be deep brown, and the apples should be tender when pierced with a knife.

Remove from the oven and cool at least 1 hour in the pan on a folded tea towel. Serve warm or room temperature, cut in wedges from the pie.