Line the bottom and sides of an 8-inch square baking pan with parchment paper, forming a sling. Grease the parchment with nonstick spray.
Combine the sugar, water, corn syrup, and cream of tartar in a heavy 4-quart saucepan and place over high heat. Stir occasionally until the sugar has dissolved and the mixture comes to a boil.
Meanwhile, combine the cream and soy sauce in a liquid measuring cup. Have this and the butter standing by.
Continue to boil the sugar syrup on high heat until it reaches 230ºF, then reduce the heat to medium and cook, without stirring, until the syrup is light golden and is approaching 300ºF, 7 to 10 minutes. At this point, there is less likelihood of crystallization, so gently swirl the pan to help break up any hot pockets.
Let the syrup continue to boil, occasionally swirling the pan, until it turns a deep amber and hits 350ºF, another 5 to 8 minutes. Remove the pan from the heat, gently swirl again to break up hot pockets, and cool for 2 minutes.
Carefully pour in the cream mixture and add the butter. Stir to combine. Return the caramel to medium heat, stir until the butter is completely melted, and continue cooking, stirring frequently, until the mixture reaches 260ºF (see note), 10 to 12 minutes. Remove from the heat and pour into the parchment-lined pan. Tap the pan gently on the counter to release air bubbles.
Cool on a wire rack for 30 minutes, then sprinkle evenly with the salt. Transfer to the refrigerator and chill until set, about 1 hour.
Use the parchment sling to remove the caramel from the baking pan. Cut into 1-inch pieces and wrap each individually in parchment. Store in an airtight container for up to 1 week.