Place the figs on a serving platter and refrigerate for 1 hour in the coolest part of the refrigerator.
Smash half of the mint leaves and set in a medium bowl. Cover with the lemon juice and let sit for 20-30 minutes. Discard the leaves. Stir the salt into the bowl of lemon juice until it dissolves. Very slowly, while whisking, pour in the heavy cream, just a little at a time. Taste and add salt if needed.
Arrange the prosciutto over the figs, and drizzle with the cream sauce. Top with the remaining mint leaves.