I have a question about the recipe "Burnt Caramel Pudding" from Midge. Any tips for finishing the cooking on the stove instead of in the oven?
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I don't see why you couldn't do this successfully on the stovetop.
I have memories of a family member making creme caramel (flan) making this with a tabletop electric pan. It's essentially the same thing, an egg yolk-based custard. I remember that electric pan had a cover, so you'd want to use that to even out the temperature and cook from above.
The key is to keep the water bath from boiling and to cook the custard long enough to set.
I quit baking/making desserts years ago, but I'd probably use the metal knife test: insert near center, if any of the custard adheres to the knife blade, it still needs more time. If it comes out cleanly, it is done.
Note that you need a thick bottomed pan to do this on a stove, one that has good heat conductivity and does not develop hot spots and a large enough burner. In an oven, the heat is more diffuse and even.
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If you read the comments, someone made it like a typical stovetop pudding after tempering the egg yolks. Personally, I think that's the way to go. She then poured it into plastic, decorative Halloween cups.