Serve these apricots with a ripe triple-creme cheese such as Pierre Robert, brought to room temperature. They are excellent over cake and ice cream, too.
Bring wine, 3/4 cup water, the sugar, cardamom, star anise, and lemon zest to a boil in a medium saucepan over medium-high heat. Cook, stirring, until sugar dissolves.
Add apricots, cover with a round of parchment, and simmer until fruit is softened and plump, about 45 minutes. Let apricots in syrup cool to room temperature.