Preheat the oven to 375°. In a large bowl, combine 1/3 cup sugar, the cornstarch and a pinch salt. Scrape the seeds from the vanilla bean into the mixture and rub with fingertips to evenly distribute. Add the pears; toss to coat.
On a lightly floured surface, roll out the crust to a 14-inch round. (If using store-bought crusts, brush 1 with water and arrange the second one on top for double thickness before rolling out.) Transfer to a parchment-lined baking sheet (some of the crust will stretch out over the edge of the parchment). Arrange the pear slices in concentric circles, leaving a 2-inch border. Fold the border over the fruit. Brush the border with cream; sprinkle with almonds and the remaining 1 tbsp. sugar.
Bake the crostata until the crust is a deep golden brown color and the fruit filling is bubbling, 45 to 50 minutes.
Transfer the crostata, on the parchment, to a rack. Let cool 10 minutes. Run a thin knife around the edges to release it from any juices stuck to the parchment. Serve the pie slightly warm or at room temperature.