Place sugar in a heavy-bottomed saucepan set over medium-high heat, stirring continuously until sugar begins to melt. Continue stirring until sugar completely melts, begins to darken, and all chunks are dissolved, about 10 minutes. Stop stirring; continue cooking until sugar begins to smoke and turns a dark shade of amber, 3 to 8 minutes. Remove from heat and wait 30 seconds.

Whisk in butter until melted and combined. Slowly pour in 1/2 cup plus 1 tablespoon cream, taking care because it can bubble over. Sprinkle in salt; stir to combine. Transfer sauce to a jar; cool completely before refrigerating.