Preheat oven to 350 degrees F (175 degrees C). Grease 15 muffin cups or line with paper baking cups.
In a large bowl, stir together the white sugar, flour, cocoa, and baking soda. Make a well in the center, and pour in the water, grape jelly, mayonnaise, and 1 teaspoon of vanilla. Mix just until blended. Spoon the batter into the prepared cups, dividing evenly.
Bake in the preheated oven until the tops spring back when lightly pressed, 20 to 25 minutes. Cool in the pan set over a wire rack. When cool, arrange the cupcakes on a serving platter.
Make the frosting while the cupcakes cool. Combine the butter, half-and-half and brown sugar in a medium saucepan. Bring to a boil, stirring frequently. Remove from the heat and stir in the confectioners’ sugar and vanilla. Set the pan over a bowl of ice water and whisk or beat with an electric mixer until fluffy. Frost cupcakes when they are completely cool.
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