I made the Chocolate Peanut Butter Cake and it was a disaster. I didn't get anywhere near enough buttercream (my first attempt split so I had to make it again and was nervous about over beating it) and the cake was dry and crumbly.
Nigella's Chocolate Peanut Butter Cake (from COOK, EAT, REPEAT) has an easy stir together chocolate sponge with a peanut butter frosting. We are not sure if the cake was the two or four layer version but as the cake batter is fairly liquid the sponge is usually very moist. If the cake was the four layer version it may be that the cake was baked for too long. The 7 minutes baking time is indicated as an approximate time and as ovens vary you may need to check the cake earlier, especially if it is a fan or convection oven as these ovens can cook more quickly even with a temperature adjustment.
It is unusual for the peanut butter frosting to split as it needs to be beaten for quite a long time and it is usually over-beating that causes curdling in whisked mixtures. We would mention that the peanut butter needs to be a regular variety (with added vegetable fat) and if you use a whole nut variety then this could cause the frosting to be thick and grainy. Also make sure that all of the ingredients are at room temperature as variations in temperature can make it more difficult for the ingredients to combine into a smooth, light frosting.