To make the meringue
Adjust an oven rack to the middle position and heat the oven to 200 degrees. Line a baking sheet with parchment paper.
Whip the egg whites, vanilla, and cream of tartar together with an electric mixer on medium-low speed in a large bowl until foamy, about 1 minute. Increase the mixer speed to medium- high and whip the whites to soft, billowy mounds, about 1 minute.
Gradually whip in 1 cup of the sugar, about 1 minute. Continue to whip the whites until they are glossy and form stiff peaks.
Using a 1/2-cup measure, scoop six 1/2-cup mounds of the meringue onto the prepared baking sheet, spaced about 1 inch apart. Gently shape each meringue into a nest using the back of the spoon.
Bake the meringues until they have smooth, dry, and firm exteriors, about 1 1/2 hours. Turn the oven off and let the meringues sit in the oven until completely dry and hard, about 2 hours.
In a large bowl, gently toss the peaches and the figs with the remaining tablespoon of sugar. Let the fruit sit at room temperature until the sugar has dissolved and the fruit is juicy, about 30 minutes.
To make the yogurt sauce
In a medium bowl whip the yogurt, vanilla, sugar and lime zest together.
To assemble, place the meringue nests on individual serving plates and spoon about 3 tablespoons yogurt sauce into each nest.
Top with about 1/2 cup of the fruit, letting some fruit and juice fall onto the plate. Serve immediately.
* This recipe works with either fresh or frozen peaches. If using frozen use 2 cups sliced peaches.