Step 1Remove the stems from the figs and cut the figs nearly in quarters, leaving them attached at the base. Press each fig at the base so the top opens out like a flower. Place each fig in a deep platter, roughly 11-by-7 inches, pressing down slightly so the fig remains upright. Scatter the slivered basil leaves over the figs. Cover with plastic wrap and let stand 30 minutes, or until ready to serve. If you want to prepare the figs ahead of time, they can be refrigerated up to two hours; let stand at room temperature one hour before serving.
Step 2In a bowl, stir together the whipping cream and lemon juice and set aside at least 30 minutes, or up to two hours. It should thicken slightly.
Step 3When ready to serve, scatter the slivered prosciutto slices over the figs. Stir the lemon cream to smooth it, then drizzle it from the tip of a spoon in a pattern of lines over the top of the figs and prosciutto. Serve immediately.