In a medium saucepan, combine the water, granulated sugar, vanilla extract, cinnamon stick, star anise, and salt. Bring the mixture to a simmer over medium heat, stirring until the sugar is fully dissolved to create a simple syrup.

Gently add the sliced peaches to the simmering syrup. Ensure the peaches are mostly submerged. If necessary, you can add a splash more water.

Reduce the heat to low, cover the saucepan partially (allowing some steam to escape), and let the peaches gently poach for 15 to 20 minutes. The peaches should become tender but still hold their shape.

Carefully remove the cinnamon stick and star anise pods from the saucepan using tongs.

Increase the heat to medium-low and cook for another 3-5 minutes, allowing the syrup to reduce slightly and thicken to a light glaze consistency. Avoid over-reducing, as the syrup will thicken more upon cooling.

Remove the compote from the heat and let it cool down to room temperature. The flavors will deepen as it cools. Serve warm or chilled over your favorite accompaniment.