Stateside, a pudding is a soft custard like food

Hmmm, more like a "milk pudding" over here, sounds like. Although the thickener isn't corn starch, more often say, rice or semolina...or even Frog Spawn (tapioca)!

We also have "steam puddings", which are suet sponge based, and absolutely wonderful winter treats. Usually topped with jam/syrup. And did I mention the importance of custard?
Let me repeat it anyway!

shanks has described Toad in the Hole below.