In a medium saucepan, heat the heavy cream until it just comes to a boil. Remove the saucepan from the heat, add the chopped ginger and stir.
Cover with a lid and allow to infuse for 30 minutes.
While the ginger is infusing in the cream, line a 9-inch loaf pan with parchment paper or foil.
After a half-hour has passed, strain the cream mixture through a cheesecloth and return infused cream to the cooled saucepan. Add 2 tablespoons butter and the sea salt, then return pan to the stove and keep warm on a low heat while you prepare the caramel.
Place a candy thermometer in a large heavy duty saucepan.
Add the corn syrup and sugar and heat, stirring gently, until all the sugar granules have dissolved. After you’ve reached a uniform, clear syrup, continue cooking it until it reaches 310 degrees F, stirring/swirling the pan ONLY as necessary (as infrequently and gently as possible) if the mixture begins to color unevenly.
When the sugar mixture has reached 310°F, remove from the heat and stir in the warm, ginger-infused cream mixture.
Be careful, as it will bubble up vigorously.
Stir until smooth (at least one minute) and then return the mixture to the heat, and cook to 248°F (firm ball). (Once when making these the temperature did not go below 250°F when I incorporated the ginger cream. I never returned it to the heat and simply stirred in the butter as instructed in the next step.)
Turn off the heat, remove the thermometer, and stir in the remaining 2 tablespoons butter.
Once incorporated, pour the mixture into your prepared pan. Cool on a wire rack.
Once caramels are cooled you can cut into desired shape. Wrapping in individual wrappers is recommended so that they do not stick together.
If you want to embellish caramels with crystallized ginger, cut into very small, very fine pieces and sprinkle 5-7 across top of caramel. Make sure they are spread out evenly over the top; if they clump together it can be overpowering.
Once wrapped and stored in a air-tight container the caramels should last 1-2 months.