From what I understand many of the pie doughs of the period were the same thing as pudding dough, everyone had a pot to boil stuff in and it was just extra if you had an oven and pie pans, sometimes with noted cooking times for a pan at the end. The that era of American cooking kind of blends puddings and pies so that they mean basically the same thing. Similar someone making a pan fried rice recipe today and just adding on the end of the recipe if you are fancy and own an actual wok you can adjust cooking times for that.
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From what I understand many of the pie doughs of the period were the same thing as pudding dough, everyone had a pot to boil stuff in and it was just extra if you had an oven and pie pans, sometimes with noted cooking times for a pan at the end. The that era of American cooking kind of blends puddings and pies so that they mean basically the same thing. Similar someone making a pan fried rice recipe today and just adding on the end of the recipe if you are fancy and own an actual wok you can adjust cooking times for that.