Make reduction. In a small saucepan, bring 1/2 cup (4 oz) to a simmer and cook until reduced by at least half and syrupy. This will take about 10 minutes and yield about 1 Tbsp of concentrated ginger essence. Set aside.
Combine 1/2 cup (4 oz) the remaining ginger juice and all other ingredients except ginger reduction in a heavy bottomed saucepan. Cook over medium heat, stirring occasionally Butter will melt and mixture will begin to boil.
Continue to cook until candy thermometer reaches 242-244 degrees F
When the correct temperature has been reached, stir in the ginger reduction and cook until thermometer comes back up to 242-244F.
Pour into parchment-lined prepared 8 x 8-inch pan. Do not scrape the bottom of the pan.
After 2 to 3 minutes, sprinkle flaky sea salt on top of caramel
Let cool, 2 to 3 hours, or harden in the refrigerator to speed up process
With a lightly oiled chef's knife or pizza wheel, cut into strips and one-inch squares.
Wrap in cellophane or waxed paper and store in airtight container for up to a month