Line a 9-inch square pan with parchment paper. For easier removal, spread a little butter on the parchment.

Put the butter, sugar and corn syrup in a large heavy-bottomed pot of at least 3 quarts. Bring to a rolling boil over medium heat.

While stirring or whisking, slowly add the sweetened condensed milk to the boiling mixture.

Continue boiling over medium heat, stirring or whisking very often, until a candy thermometer reads 235–240°F. This part takes about 25–30 minutes. Do not walk away for long, and whisk more attentively as the mixture gets close to the target.

Remove from the heat, stir in the vanilla extract and immediately pour into the prepared pan.

Let cool for about 30 minutes, then sprinkle with coarse salt if using. Cool completely. Refrigerating for at least 1 hour before cutting makes the caramel easier to work with.

Cut into small pieces with a long, sharp knife. Wrap individually in parchment or candy papers and store in an airtight bag or container.