1) Preheat the oven to 350°F. Lightly grease and flour (or grease, then line with parchment, then grease again) two 8" x 2" round cake pans. Note: These pans need to be at least 2" tall; if you have non-standard, shorter 8" pans, substitute 9" round pans.
2) To make the cake: Whisk together the dry ingredients. Add the eggs, oil, and vanilla, beating until smooth.
3) Gradually add the water, beating until smooth.
4) Pour the batter into the prepared pans.
5) Bake the cakes for 35 to 38 minutes (a bit less if you use a 9" pan), or until a cake tester inserted into the center comes out clean. Cool the cakes in the pan for 15 minutes, then turn them out of the pans to cool completely on a rack.
6) To make the filling: Mix the sugar, peanut butter and vanilla till crumbly. Add the milk and mix till smooth, adding more milk if necessary to make a spreadable filling.
7) Divide the cooled layers in half horizontally, to make four layers. Place one layer on a serving plate, and spread with filling. Repeat with the next two layers. Top with the final cake layer.
8) To make the icing: Combine the chocolate chips, cream, and corn syrup in a microwave-safe measuring cup. Microwave till the cream is very hot, and the chips are soft.
9) Stir till the chips melt, and the mixture is smooth.
10) Spread the icing atop the cake, letting it drizzle down the sides.
11) Serve in thin slices; the cake is very rich.
12) Yield: one 8" layer cake, about 12 to 16 servings.