Preheat oven to 325° with a rack in the middle. Grease a 9-in. springform pan and line with parchment paper, cut to fit.
Heat chocolate in a double boiler or metal bowl set over (not in) a pot of simmering water until about half-melted. Remove pan from heat and stir until smooth. Stir in oil. Cool slightly; stir in 2 tsp. vanilla.
Grind pecans and 1 tbsp. granulated sugar in a food processor in 2 batches, pulsing so you don't end up with pecan butter (you'll have some larger pieces). With a medium-mesh sifter, sift to yield 2/3 cup pecan flour.
Zest 2 oranges with a 5-holed zester; juice enough oranges to yield 1 1/4 cups juice.
Using a mixer, beat egg yolks and brown sugar in a medium bowl until mixture is pale and, when beaters are lifted, falls in thick ribbons, 5 minutes. Beat in 2 tbsp. plus 1 tsp. orange juice (mixture will get more liquidy). Gently fold in pecan flour. Fold in chocolate mixture.
In another bowl with clean beaters, beat egg whites with salt until foamy. Gradually rain in 7 tbsp. granulated sugar; beat into soft peaks, 3 minutes. Gently fold half of egg whites into chocolate mixture; then fold in remaining whites.
Pour batter into pan and bake until a toothpick inserted in center comes out with crumbs adhering, 1 to 1 1/4 hours. Let cool on a rack (it will sink a lot).
Make glaze: In a large frying pan, boil remaining orange juice, 2 tbsp. granulated sugar, and the zest over medium-high heat until reduced to 1/2 cup, 10 minutes. Sift powdered sugar into juice and whisk smooth. Let cool 5 minutes, then whisk in remaining 1 tsp. vanilla.
Let cake cool, then run a heated thin metal spatula (heat under hot water, then dry with a towel) around inside of pan.
Remove rim of pan. Starting from edge and working toward center, carefully trim uneven top layer from cake using a large serrated knife. Invert cake onto a plate.
Cut cake with a heated knife, wiping between slices. Drizzle slices with glaze.
*Find nut flours at amazon.com (pecan flour is called "meal").