Line a 9-by-13-inch baking pan with heavy-duty foil, allowing ends to overhang by 1 inch.
In a large, heavy pot, combine sugar, 1 cup cream, corn syrup and butter. Cook over medium heat, stirring, until butter has melted and sugar has dissolved. Increase heat to high and bring to a boil. Cook, without stirring, until mixture reaches 248F on a candy thermometer, 25 to 30 minutes.
Combine remaining 1 cup cream and vanilla; carefully pour into caramel mixture (be careful, as mixture may bubble up). Cook until mixture returns to 248F on candy thermometer, about 10 minutes.
Pour into lined baking pan.
Sprinkle with coarse salt, if desired. Cool slightly, then cover with plastic wrap and let stand at room temperature for at least 4 hours or overnight.
Place a sheet of parchment on a countertop and turn slab of caramel out onto parchment. Peel off foil.
Cut slab crosswise into 10 strips, then cut each strip into 5 caramels.
