Preheat the oven to 350 F and grease a 9x13-inch baking dish.
Sift the flour, soda, and salt together into a medium-sized bowl. Set aside.
Using a handheld or stand mixer, beat the eggs with the sugar until light and fluffy. Beat in the peach jam and vanilla extract.
Add the melted butter and vinegar.
Add the flour mixture and milk to the egg mixture until fully incorporated.
Pour the batter into the prepared baking dish and bake for 30-40 minutes or until a toothpick inserted in the middle comes out clean.
While the pudding is baking, prepare the sauce: in a small saucepan melt together the butter, sugar, heavy cream, water, and vanilla extract.
Pour the hot sauce over the pudding as soon as you take it out of the oven. Serve warm.