Line the bottom and sides of an 8-inch square pan with parchment paper.
Combine the sugar, water, corn syrup, and cream of tartar in a heavy 4-quart saucepan and put over high heat. Stir occasionally until the sugar has dissolved. Cover and continue to cook for 5 minutes.
Meanwhile, combine the heavy cream and soy sauce in a liquid measuring cup. Have this and the butter standing by.
Remove the lid from the sugar mixture, and attach a candy thermometer to the side of the pan. When the sugar mixture reaches 230 degrees F, reduce the heat to medium and cook, without stirring, until the syrup is a golden color and is approaching 300 degrees F, about 6 to 7 minutes. At this point, there is less likelihood of any crystallization, so gently swirl the pan to break up any hot pockets.
When the temperature approaches 350 degrees F, it will turn deep amber. Remove the pan from the heat, and gently swirl again to break up all of the hot pockets. Cool for 2 minutes.
Carefully incorporate the cream and soy mixture and the butter into the pan. Stir to combine. Return the caramel to medium heat, stir until the butter is completely melted, and continue cooking until it reaches 255 degrees F. Remove from the heat and pour into the parchment-lined pan, tap gently to release air bubbles.
Cool on a cooling rack for 30 minutes, and then sprinkle evenly with the salt. Continue cooling on the rack for an additional 3 1/2 hours. Cut into 1-inch pieces and wrap individually in parchment. Store in an airtight container for up to a week.