Summer Peach Pie with Vanilla and Cardamom

Position rack in bottom third of oven and preheat to 400 °F. Combine 2/3 cup sugar and vanilla bean in processor; blend until vanilla bean is very finely minced. Sift vanilla sugar through strainer into large bowl; discard any large bits in strainer. Mix flour and cardamom into vanilla sugar. Add peaches to flour-sugar mixture and toss gently to coat. Roll out 1 pie crust disk on floured surface to 12-inch round. Transfer to 9-inch-diameter glass pie dish. Trim dough overhang to 1/2 inch. Spoon peach mixture into crust; dot with butter. Roll out second pie crust disk on lightly floured surface to 12-inch round. Drape dough over peach filling; trim overhang to 1 1/2 inches. Fold top and bottom edges under, pressing together to seal. Crimp edges decoratively. Using small sharp knife, cut 2-inch-long X in center of top crust to allow steam to escape. Brush crust lightly with whipping cream; sprinkle with remaining 2 teaspoons sugar. Place pie on rimmed baking sheet. Bake until crust is golden, peaches are tender, and juices bubble thickly through cut in top crust, about 1 hour 15 minutes. Transfer pie to rack and cool until lukewarm, about 2 hours. Serve pie lukewarm or at room temperature with vanilla ice cream.