Prepare 4-6 small serving glasses or ramekins. Set aside.
In a medium saucepan over medium heat, combine heavy cream, granulated sugar, lime zest, and salt. Stir until sugar dissolves, about 3-4 minutes.
Bring mixture to a gentle boil, then reduce heat to medium-high. Simmer for exactly 5 minutes, stirring constantly. Mixture will reduce slightly and coat the back of a spoon.
Remove from heat and let cool for 10 minutes. Stir in fresh lime juice and vanilla extract. Mixture will begin to thicken immediately.
Pour through a fine-mesh strainer to remove zest bits for smooth texture.
Divide posset mixture evenly among serving glasses. Cover with plastic wrap and refrigerate for at least 4 hours, or ideally overnight.
For optional crumble topping: Mix crushed graham crackers, brown sugar, and melted butter. Toast in 350°F oven for 5-7 minutes until golden. Cool completely.
Serve chilled, topped with graham cracker crumble, extra lime zest, and fresh lime wedges.