Preheat oven to 350°F. Grease two 9x2 inch round pans and line bottoms with parchment. Grease parchment.
In a microwave safe bowl, combine the chopped chocolate, oil, and cocoa powder. Melt chocolate by heating at 50% power for 2 minutes, stopping halfway through to stir. Be careful not to overheat, and be sure to do a lot of stirring so that chocolate melts from residual heat. Set aside to cool slightly.
In another bowl, mix together flour, baking soda, baking powder, and salt.
In a mixing bowl, whisk together the eggs, then whisk in the sugar and vanilla extract. Gradually whisk the chocolate mixture into the egg mixture.
Add flour mixture alternately with the milk, beating by hand with a heavy duty scraper (or using an electric mixer on low speed) until fully blended.
Divide batter between pans and bake on middle rack until a tester inserted in center comes out clean. For 9-inch pans, this should take about 30 minutes, but it might vary from oven to oven.
Set the pans on a wire rack and let layers cool for about 10 minutes in the pans.
Loosen edges with a knife and invert layers onto racks. Carefully remove parchment paper and let cool completely.