In a mixing bowl stir together flour, the 1/2 cup sugar, the 2 tablespoons cocoa powder, and baking powder. Add the milk, oil, and vanilla; stir until batter is smooth. Stir in the peanut butter pieces. Spread batter evenly in the bottom of a greased 3-1/2- or 4-quart crockery cooker.
In another mixing bowl combine the 3/4 cup sugar and the 1/4 cup cocoa powder. Stir together boiling water and peanut butter; stir into the cocoa mixture. Pour evenly over the batter in the crockery cooker.
Cover; cook on high-heat setting for 2 to 2 1/2 hours or until a toothpick inserted 1 inch into the center of the cake comes out clean. Let stand, uncovered, for 30 to 40 minutes to cool slightly.
To serve, spoon pudding cake into dessert dishes. Sprinkle with peanuts. If desired, serve with ice cream.