Bring the sugar and 3 tablespoons water to a boil over medium-high heat without stirring. Cook until it reaches a pale amber caramel, 5 to 7 minutes.
Remove from the heat and carefully add the wine and thyme sprigs. Cook, stirring to soften the caramel, until it is reduced to the desired consistency, 5 to 7 minutes. Cool to room temperature. Serve over pistachio ice cream and garnish with chopped pistachios.
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