Adjust oven rack to middle position and preheat oven to 325 degrees F. Lightly grease 9-inch springform pan with oil. Feel free to line the bottom of the pan with parchment paper, if desired.
Create a double-boiler with a medium size heat-proof bowl set on top of a saucepan of simmering water. Melt the butter and chocolate in the bowl. Alternatively, microwave butter and chocolate in a medium bowl at 50 percent power, stirring often, until melted, 1½ to 2 minutes. Stir in vanilla and set aside.
Using a stand mixer fitted with whisk attachment, whip egg whites on medium-low speed until foamy, about 1 minute. Or use a hand mixer. Increase speed to medium-high and continue to whip, slowly adding ½ cup granulated sugar, until whites are glossy and thick and hold stiff peaks, about 4 minutes longer. Transfer whites to a large bowl.
Add egg yolks and remaining ½ cup granulated sugar to now-empty mixer bowl and whip on medium-high speed until thick and pale yellow, about 3 minutes, scraping down bowl as necessary. Add chocolate mixture and mix on medium speed until incorporated, about 15 seconds. Add almond flour, cocoa, and salt and mix until incorporated, about 30 seconds.
Remove bowl from mixer and stir a few times with a large silicone spatula, scraping the bottom of the bowl to make sure almond flour is fully incorporated. Add one-third of whipped whites to bowl, return bowl to mixer, and mix on medium speed until no streaks of white remain, about 30 seconds, scraping down bowl halfway through mixing. Add remaining whites to the bowl. Using a large silicone spatula, gently fold whites into batter until no streaks of white remain. Pour batter into the prepared pan, smooth top with spatula, and place pan on rimmed baking sheet.
Bake until a toothpick inserted in the center comes out with a few moist crumbs attached, about 50 minutes, rotating pan halfway through baking. Let the cake cool in the pan on a wire rack for 20 minutes. Run a thin knife around the edge of the cake to loosen and remove the side of the pan. Let cake cool completely, about 2 hours. (Cake can be wrapped in plastic wrap and stored at room temperature for up to 3 days.)
Dust top of cooled cake with confectioners' sugar, if using.