Score a cross shape in the bottom of each peach. Put the peaches into a large pot of boiling water, for 30 seconds, then transfer the peaches to a large bowl filled with cold water to refresh. Set aside for another 40 to 45 seconds, then drain the peaches, and peel using a sharp knife.
Put the measured cold water, cinnamon, whole star anise, ginger slices, and sugar into a large saucepan, stir well, and bring to a boil. Reduce the heat, and simmer the mixture, stirring occasionally, until the sugar has dissolved and the mixture resembles syrup.
Add the peaches to the syrup mixture, and cover them with a disk of greaseproof or parchment paper measuring the same diameter as the pan. Cover the pan with a lid, reduce the heat to a simmer, and simmer for 15 to 20 minutes, or until the peaches are cooked through (they will be soft when pricked with a knife.) Remove the peaches, and set aside on a warm plate. Continue to boil the syrup until its volume has reduced to about 1 cup. Set aside to cool.
Brush the peaches with a little of the syrup. Stir half of the remaining syrup and the ground star anise into the Greek-style yogurt until well combined, adding more syrup as necessary, to taste.
To serve, cut each of the spiced poached peaches in half and place 2 of the peach halves onto each of the serving plates. Spoon a portion of the star anise yogurt alongside each peach. Drizzle a little syrup over each peach. Sprinkle over the toasted almonds.