Toasted Nut Tart

Name: Toasted Nut Tart
Ingredients: 1 cup all-purpose flour plus more for surface; 2 tablespoons cornstarch; 1/2 teaspoon kosher salt; 1/4 teaspoon baking powder; 1/4 cup (1/2 stick) unsalted butter, room temperature, cut into 1/2 cubes; 1/4 cup sugar; 2 tablespoons powdered sugar; 1 large egg; 1/2 cup natural unsalted pistachios, coarsely chopped; 1/2 cup toasted hazelnuts, skins rubbed off, coarsely chopped; 1/4 cup pine nuts; 1/4 cup (1/2 stick) unsalted butter; 1 cup (packed) dark brown sugar; 1 cup light corn syrup; 1 teaspoon kosher salt; 1 teaspoon vanilla extract; 3 large eggs; Powdered sugar (for dusting); Pistachio or hazelnut gelato (optional); A 9-diameter tart pan with a removable bottom