Preheat the oven to 350°.

In a 9x13 pan, place:

   - 1 stick butter (1/2 cup)

Put the 9x13 pan in the oven for the butter to melt.

Put on to boil:

   - 2 cups water

In a large bowl, mix together with a whisk:

   - 1 1/4 cups sugar

   - 1/3 cup cocoa powder

   - 2 tsp baking powder

   - 3/4 salt

Add to the sugar mixture:

   - 1 cup milk

   - 2/3 cup creamy peanut butter

   - 2 tsp vanilla

Stir until no dry streaks remain. Batter will be thick.

If the butter has completely melted, remove the baking dish from the oven and tilt it so the butter coats the entire bottom and sides of the pan. Add the batter to the pan and spread into an even layer. Do not stir. (Butter may pool in the corners.)

For the topping, mix together with a whisk:

   - 3/4 cup sugar

   - 1/4 cup cocoa powder

   - 1/4 cup brown sugar

Sprinkle the topping evenly over the batter. Do not stir.

Over the topping, sprinkle:

   - 1/2 cup semisweet chocolate chips

Over everything, pour the boiling watter. Do not stir.

Bake until set around the edges and the center remains wet and jiggly. Start checking it after 20 minutes.

While it cools (for at least 10 minutes), melt:

   - 1/2 cup creamy peanut butter

Drizzle the peanut butter over the cake.