Coat the inside of a 2 1/2 quart to 5 quart slow cooker or crock pot with cooking spray. (Note: the cake’s cooking time and final appearance will vary depending on your crock’s size.)
Whisk together the flour and baking powder in a medium bowl and set aside.
In a large bowl, melt the butter and chocolate in the microwave or over a pan of simmering water and mix well.
Whisk in the 2/3 cup sugar, 3 tablespoons of cocoa, vanilla, salt, milk, and egg yolk.
Add the flour mixture and stir until thoroughly mixed.
Pour the batter into the slow cooker and spread it evenly.
In a medium bowl, whisk together the the ‘liquid on batter’ sugar, brown sugar, cocoa and hot water until the sugar is dissolved.
Pour the mixture over the batter in the slow cooker.
Cover and cook on high for 1 ¼ to 2 ¼ hours, depending on size of the crock pot.
Even when done, the cake will be very moist and floating on a layer of molten chocolate, but you will know it is ready when nearly all of the cake is set and the edges begin to pull away from the sides of the pot.
(As you check, try not to let the condensed steam from the lid, drip on the cake.) When it is done, turn off the power and remove the lid.
Let it cool for 25 minutes, then serve it in bowls topped with whipped cream or ice cream.