Make the dough. In a 4-quart / 4 L bowl, beat 170 g softened butter with 100 g brown sugar and 50 g granulated sugar on medium speed for 2 to 3 minutes, until pale and fluffy. Beat in the egg and 1 tsp vanilla. Whisk 240 g flour, 1/2 tsp baking soda and 1/2 tsp salt together, then mix it in on low speed until no dry streaks remain.
Make the caramel. In an 18 cm / 7-inch (2-quart / 1.9 L) heavy-bottomed saucepan, stir 100 g sugar with 2 tbsp water over medium heat until the sugar dissolves, then stop stirring. Cook for 6 to 8 minutes, swirling the pan now and then, until the syrup turns deep amber, the color of an old copper penny. Take it off the heat and whisk in the 60 ml cream (it will bubble up), then the butter, tamarind paste and 1/4 tsp salt. Simmer on low for 1 minute until smooth.
Chill both. Scrape the caramel into a small heat-proof bowl and wrap the dough in plastic. Refrigerate both for 45 minutes, until the caramel is thick like soft fudge and the dough feels firm.
Heat the oven to 175 C / 350 F with racks in the upper and lower thirds. Line two 33 x 46 cm / 13 x 18-inch sheet pans with parchment. Weigh the dough into 12 portions of about 50 g each.
Fill the cookies. Flatten one portion in your palm into a 7 cm / 3-inch disk, set a heaping teaspoon of chilled caramel in the middle, then pinch the edges closed and roll into a ball. Place the balls seam-side down, 6 per pan, 5 cm / 2 inches apart.
Bake for 12 minutes, swapping the pans between racks and turning them at the 6-minute mark, until the edges are golden and set and the tops still look slightly soft. Sprinkle each cookie with flaky salt right away.
Cool the cookies on the pans for 5 minutes, then move them to a wire rack. Spoon any leftover caramel into a jar and refrigerate it.