To Make the Meringues

Preheat the oven to 200°F. On 2 pieces of parchment paper, trace thirty-two 2-inch circles, 1 inch apart. Place the parchment paper, marked side down, on baking sheets. (Placing them pencil side down will prevent marks on the meringues. You will be able to see the outline of the circles when they are inverted.)

With an electric mixer, whisk the egg whites on medium speed until frothy. Add 1 tablespoon of the granulated sugar, increase to medium-high speed with a stand mixer (high speed with a hand-held mixer), and whip until soft peaks form. Add 3 tablespoons of the granulated sugar and continue to whip until stiff, satiny peaks form. Sift together the remaining 2 tablespoons granulated sugar, the confectioners’ sugar, and instant espresso or coffee. Fold the dry ingredients into the egg whites.

Place a ¼-inch plain pastry tip in a pastry bag and fill the pastry bag with the meringue (pastry bag tips). Starting from the inside of each circle, pipe the meringue in a solid spiral, filling the circle. Pipe the remaining circles in the same manner. (If you don’t want to use a pastry bag, you can carefully spread the meringue into circles with a small offset spatula or the back of a spoon. Use a scant tablespoon for each.)

Bake the meringues until dry, about 5 hours, though you can leave them in the oven overnight. To test if they are done, remove the pan from the oven and let sit on the counter for 30 seconds. Try to remove a meringue from the baking sheet. If it peels off the parchment paper easily, the meringues are done. Let cool for 15 minutes and then put in an airtight container until you are ready to assemble the sandwiches.

To Make the Ice Cream

Whisk the coconut cream in a medium bowl until smooth. Whisk in the coconut milk, cream, sugar, and salt. Refrigerate for at least 2 hours or up to overnight. Put the coconut in a bowl and put the bowl in the freezer. Churn the ice cream base in an ice cream machine according to the manufacturer’s instructions. Fold the ice cream into the toasted coconut. Freeze until scoopable, about 4 hours, depending on your freezer.

In Advance

The meringues can be made up to 3 days in advance as long as the weather is not too humid. I often store meringues in a turned-off oven. Otherwise, they should be stored in an airtight container. The ice cream can be made 2 days in advance. The sandwiches can be assembled 2 days in advance. Store well wrapped in plastic wrap.