Heat oven to 225°F. Line two baking sheets with parchment paper.
Place the jelly beans in the food processor and process for one minute, or until finely chopped.
Combine the egg whites and cream of tartar in the bowl of a stand mixer fitted with the whisk attachment; beat until foamy. Increase the speed to high and gradually add ½ cup sugar until stiff and glossy peaks form, about 2 to 3 minutes. Fold in the chopped jelly beans with a rubber spatula.
Drop the meringue mixture into mounds on the baking sheet. Bake until firm and dry, 75 to 90 minutes. Cool completely on the baking sheet.
Meanwhile, beat the heavy cream in the bowl of a stand mixer until it begins to thicken. Add 1 tablespoon sugar and continue to whip until soft peaks form.
Add a dollop of whipped cream to the flat side of 12 of the meringues. Form sandwiches with the remaining 12 meringues.
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