Pulse 30 gingersnap cookies in a food processor until finely ground. Add 5 Tbsp melted butter and 7 tsp brown sugar; pulse until mixture has the texture of wet sand. Press into the bottom and sides of a 9-inch springform pan (or pie dish). Freeze until firm about 30 minutes.

Sprinkle 2 packets of unflavored gelatin over 1/4 cup cold water; let stand until softened. Set aside.

In a large saucepan, combine peaches, lime juice, 1/2 cup sugar, 2 basil leaves, 1/4 cup water, 1/2 cup peach juice, and 1/2 tsp salt. Bring to a boil, then cover, reduce heat to medium-low, and simmer until peaches are very soft, about 15 minutes. Strain through a fine-mesh sieve, pressing on solids to remove as much liquid as possible (discard solids). Stir in gelatin until dissolved. Freeze until thickened slightly, about 1 hour.

Beat 1.25 cups heavy whipping cream with 1/4 cup honey, and 1/2 tsp vanilla until soft peaks form. Gently fold whipped cream into chilled peach puree. Pour mixture into crust and freeze until firm, at least 4 hours and up to 1 day.

To make sugared basil leaves: Whisk 1egg white with 1 teaspoon water until frothy. Brush a thin layer of egg wash onto basil; sprinkle with sugar. Transfer to a wire rack and let cool until firm and dry, about 1 hour. Leaves can be stored in an airtight container at room temperature up to 1 day.

Remove from freezer 15 to 20 minutes before serving.

Beat 1/4 cup heavy whipping cream with 1 tsp honey for 1 minute on low speed, increasing to medium for 2 minutes until soft peaks form.

Top with whipped cream, additional peach slices, and sugared basil leaves; cut into slices to serve. Freeze leftovers.