The yogurt in this dish is drained overnight, which gives it a rich, dense consistency. The fruit may also be poached the day before serving, and chilled in its poaching liquid.
Line a sieve with a double thickness of cheesecloth, and place over a bowl. Place yogurt in cheesecloth, and wrap securely. Allow to drain overnight in refrigerator.
Peel pears, cut in half lengthwise, and pour lemon juice over them. Place pears cut-side down in a large saucepan. Add dried figs, apricots, cherries, wine, cinnamon, star anise, and vanilla bean and seeds. Cover, and bring to a simmer over medium heat. Cook over low heat for 10 minutes, until pears are soft when pierced with a knife but still hold their shape. Uncover; allow fruit to cool in the liquid.
Remove core from pears using a melon baller. Arrange pear half, dried fruit, and yogurt in compote dishes. Strain remaining poaching liquid, and discard the solids. Drizzle compotes with poaching liquid, and serve.