Preheat the oven to 110°F (43°C). Line 2 baking sheets with parchment paper. Lightly rub the parchment sheets with unsalted butter, and then lightly dust with cornstarch. In a large bowl, beat the egg whites and cream of tartar until stiff, about 2 minutes. Add the sugar slowly to the egg white mixture and continue beating until stiff, glossy peaks form, about 5 minutes.
Place half the mixture in a pastry bag with a 1/4 inch tip. Pipe out 1-inch meringue rounds, 1/2-inch apart, onto the prepared baking sheets. Place the meringues in the oven and bake until they're firm to the touch, lift off the parchment easily, and dry underneath, 80 to 95 minutes. Open the door of the oven for 10 seconds every 15 minutes while baking to release any built up moisture and help the meringues stay dry and crisp.
Remove the meringues from the oven. Slide the meringues still on their parchment onto a wire rack to cool. When the baking sheets are cool, line them with new parchment and repeat the process until all of the meringue mixture has been used.
In a medium bowl, whip the heavy cream and the confectioners' sugar until thick.
Peel all the meringues off the parchment sheets and place on a dry work surface. Turn 24 meringue halves upside down and make 2 rows of 12. Spoon the whipped cream into a pastry bag and pipe out approximately 1 teaspoon of whipped cream in the middle of each meringue. To assemble, take the remaining meringues and place one on top of each meringue to make sandwiches. Press each sandwich together gently.
Place each cookie in an individual paper pastry cup and refrigerate until serving. The Little Clouds will keep refrigerated for up to 3 days in a tightly covered container.