Heat oven to 375°F (190°C); parchment-line sheets.
Whisk flour, cream of tartar, baking soda, and salt in bowl; set aside.
Beat butter and 1 1/2 cups sugar about 2 minutes until fluffy; add eggs individually, then vanilla.
Mix in soy sauce and caramel; gradually add dry to form dough.
Scoop tablespoons; coat in remaining 3 tbsp sugar and place 2 inches apart.
Bake 9–11 minutes until edges set and centers slightly soft. Cool on sheet 5 minutes; transfer to rack.
Once cool, drizzle extra caramel and sprinkle flaky salt.