Preheat oven to 350 degrees F. Butter a 9 x 5 x 2-inch gratin dish or a 10-inch round deep pie plate or porcelain dish. Dust dish with flour. Scrape seeds from vanilla bean into large bowl. Add eggs. Using electric mixer, beat until frothy. Add sugar and beat until mixture thickens. Add flour and beat until thick and smooth. Mix in cream, crème fraîche, or yogurt, milk, anise, and salt. Set batter aside while preparing the pears.

Cut the pears into sixths or eighths, remove the cores. Layer pear slices attractively in the bottom of the prepared dish. Sprinkle pears with eau du vie, if you like. Pour the batter over, leaving just a little of the tops of the pears peeking through.

Bake until the clafouti is nicely browned on top and a knife inserted into it comes out clean, about 20 minutes. Sift confectioners' sugar over clafouti and serve warm or at room temperature.