Combine sugar, water, and salt in a medium saucepan over medium heat. Stir gently until mixture comes to a simmer. Simmer, without stirring, until syrup is honey-colored, shaking as needed to prevent scorching, about 5 minutes. Continue cooking until syrup has darkened to an amber color. Add cream and reduce heat to low. Cook, stirring continuously, until thickened, about 3 minutes. Remove from heat and stir in vanilla extract. Transfer to a heatproof container and let cool.

To assemble, scoop ice cream into waffle cones. Press popcorn onto the sides of the ice cream. Drizzle with caramel sauce and sprinkle with chocolate shavings.