Place sugar in a heavy-bottomed saucepan set over medium-high heat. Stir continuously until sugar begins to melt. Continue stirring until the sugar melts completely, begins to darken and all the chunks are dissolved, about 10 minutes. Stop stirring and continue to cook until the 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 and stir to combine. Transfer sauce to a jar and cool completely before refrigerating.