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Step 1
Get ready. Position a rack in the center of the oven and preheat the oven to 350°F. Line the bottom of a 9-inch springform pan with a round of parchment paper.
Step 2
Melt the chocolate. Fill a medium pot halfway with water and bring to a simmer. Place a medium heat-safe bowl over the pot of simmering water and make sure the bottom of the bowl does not touch the water. Add the chocolate and olive oil to the bowl. Use a rubber spatula to stir continuously until the chocolate has melted and it’s fully combined with the oil. Remove the bowl from the heat and stir in half the sugar, the cardamom, and almond extract. Set aside and allow the chocolate to cool.
Step 3
Meanwhile, separate the eggs. Place the whites in a medium bowl and the yolks in a small bowl.
Step 4
Whip the egg whites. Use an electric hand mixer fitted with the whisk attachment to whip the egg whites on medium-high speed until frothy and opaque in color, 3 to 5 minutes. Slowly add in the remaining sugar and beat until the whites become thick, glossy, and have stiff peaks, about 3 to 5 minutes.
Step 5
Make the batter. When the chocolate has cooled a bit, whisk the egg yolks one at a time into the chocolate, until fully combined. Then use a rubber spatula to fold one-fourth of the beaten egg whites into the chocolate batter—you just want to lighten the batter a bit. Now, fold the rest of the egg whites into the chocolate mixture by drawing the spatula around the side and up through the center of the chocolate. Do this until the whites are fully incorporated and you have a thick, cohesive batter.
Step 6
Bake the cake. Transfer the batter to the prepared pan and bake for 25 to 30 minutes, until the top has puffed up and looks dry—it might even crack a little bit.
Step 7
Cool the cake. Let the cake cool in the pan on a rack for about 1 hour. It will deflate and the top will crack. It’s okay! That’s what it’s supposed to do. When the cake has cooled completely, release it from the springform pan. If it looks like the cake might stick to the sides, run a knife around the sides before releasing it from the pan.
Step 8
Finish and serve. The cake will have a crackled top and a fudgy middle. Dust the cake with powdered sugar or cocoa powder and serve with berry compote, if desired.