Heat oven to 350° F with the rack in the lowest position.
Place the dough on a floured work surface. With a floured rolling pin, roll the dough into a 10-inch circle. Fit the dough into a 9-inch tart pan. Roll the rolling pin over the top edge of the pan to remove the excess dough. Refrigerate until chilled, at least 30 minutes.
Meanwhile, cook the sugar and 1/3 cup water in a medium pot over medium heat, stirring, until the sugar is just dissolved, 2 to 3 minutes. Continue to cook, without stirring, until the syrup is a golden brown, 14 to 16 minutes more. (If dark spots start to appear in the syrup, gently swirl the pan to incorporate them.) Remove from heat and carefully add the cream, butter, and salt (the mixture will sputter); stir until combined. Stir in the walnuts.
Transfer the mixture to the chilled tart crust and place on a rimmed baking sheet. Bake until the crust is golden brown, 45 to 55 minutes.
Cool in the pan for 15 minutes, then carefully remove the sides of the pan. Cool completely. (Place the bottom of the pan back into the sides to transport the pie safely.)
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