- 2 tablespoons sugar
- 1 tablespoon fresh lime juice
- Large pinch of salt
- 3 Bosc pears (about 1 1/2 pounds total), peeled, quartered, cored, cut into 1/2-inch cubes
- 1 cup plus 1 tablespoon all purpose flour
- 1/4 cup cornstarch
- 1/2 teaspoon salt
- 1/2 teaspoon (scant) baking powder
- 1/4 teaspoon baking soda
- 1/8 teaspoon ground allspice
- 1/8 teaspoon ground ginger
- 1/8 teaspoon ground black pepper
- 1/8 teaspoon ground whole star anise
- 1/2 cup (1 stick) unsalted butter, room temperature
- 3/4 cup sugar
- 2 large eggs
- 1 3-inch piece vanilla bean, split lengthwise
- 1/4 teaspoon finely grated lime peel
- 3/4 cup buttermilk
- Powdered sugar
- 1 1/2 cups crème fraîche
- Mix sugar, lime juice, and salt in heavy large saucepan. Add pears and toss gently to coat. Cover and cook over medium-low heat until pears are just tender, stirring occasionally, 10 to 12 minutes. Transfer mixture to bowl. DO AHEAD: Can be made 1 day ahead. Chill until cold, then cover and keep chilled.
- Preheat oven to 350°F. Butter and flour 9-inch-diameter cake pan with 2-inch-high sides; line pan with round of parchment paper. Sift first 9 ingredients into medium bowl. Using electric mixer, beat butter in large bowl until fluffy. Gradually add sugar, beating until smooth. Beat in eggs 1 at a time, beating to blend between additions. Scrape in seeds from vanilla bean and add lime peel; beat to blend. Beat in flour mixture in 4 additions alternately with buttermilk in 3 additions, scraping down bowl occasionally. Transfer batter to prepared pan.
- Bake cake until beginning to brown on top and tester inserted into center comes out clean, about 30 minutes. Cool cake in pan on cooling rack. DO AHEAD: Cake can be made 1 day ahead. Cover and let stand at room temperature.
- Cut around pan sides to loosen cake. Turn cake out onto rack; peel off parchment and turn right side up onto platter. Sift powdered sugar over. Cut into wedges. Serve with pear compote and dollop of crème fraîche.
- A brown, star-shaped seedpod that's available in the spice section of some supermarkets and at specialty foods stores and Asian markets.
- Available at most supermarkets and at specialty foods stores.