Preheat the oven to 350F (180C) and line a 12-cavity muffin pan with muffin papers. You will end up with about 16-18 cupcakes in total, so you will need 2 pans.
Add the finely chopped chocolate to a heat proof bowl. Microwave for 45-second intervals on medium power (not high power, which is typically the default). Stir between each interval until melted. Alternatively, melt in a double boiler over low heat. Set aside.
In a medium bowl, whisk together the flour, cocoa, baking powder, baking soda and salt. If the cocoa powder is lumpy, sift it first. Set aside.
In a large bowl, whisk together the oil, granulated sugar and brown sugar until you no longer see clumps/lumps of brown sugar.
Whisk the melted chocolate and vanilla extract into the oil and sugar mixture until smooth - you will still have granules of brown sugar, which is totally fine.
Whisk the eggs into the oil, sugar & chocolate mixture. I always do this by hand, but an electric mixer on low speed works too. Be careful not to over mix if using an electric mixer.
Whisk in the sour cream, followed by about ⅓ of the flour mixture.
Then whisk about ½ of the milk into the bowl, followed by about ⅓ more of the flour mixture. Whisk in the final ½ of the milk, followed by the rest of the flour mixture until smooth.
Spoon the cupcake batter into the prepared pans, filling each cupcake liner about ½ to ⅔ full. Do not fill ¾ full or to the top of the cupcake liner. If you only end up with 12 cupcakes in total, your liners are too full and your cupcakes can overflow and sink as they bake.
Bake 1 tray of cupcakes in the middle of the preheated oven. They will bake for about 17-20 minutes, or until the tops look set and an inserted toothpick comes out clean or with a few muffin crumbs. A toothpick should not have muffin batter on it.
Cool the cupcakes in pan for about 10 minutes, then transfer to a wire cooling rack to continue cooling.