Warning: do not walk away from your caramel because it will probably burn the second you walk away from it (trust me).
In a heavy bottomed saucepan over medium heat, add the sugar and stir every 1-2 minutes or so until it begins to melt (the sugar will start to clump up before melting).
Once the sugar is completely melted and smooth (it should be an amber color), immediately remove from the heat. This should take about 10-15 minutes.
Stir in the butter until combined (don’t be scared if it bubbles a lot).
Add in the heavy cream and salt and mix until fully combined and smooth. It won't want to combine at first, but just keep stirring and it will come together.
Pour the caramel into a heavy glass jar to cool to room temperature. The caramel will thicken as it cools.
Can be stored in the fridge for up to a month! The caramel will get hard in the fridge, so you can microwave it for intervals of 15 seconds to get it back to a pourable consistency.
Notes
For vegan caramel: Instead of butter, just use vegan butter and use coconut cream instead of heavy cream!For thicker caramel: Reduce the heavy cream to ⅓ cup for thicker caramel (or even ¼ cup for super stiff caramel).For thinner caramel: Add heavy cream 2 tablespoons at a time until desired consistency.Use brown sugar or brown butter for even more depth of flavor!