Pear and Almond Tart

Name: Pear and Almond Tart
Ingredients: 4 cups water; 1 1/4 cups sugar; 1 1/2 tablespoons fresh lemon juice; 3 medium-size firm but ripe Bosc pears, peeled (each about 7 ounces); 1/2 cup powdered sugar; 1/4 cup blanched slivered almonds; 1/4 teaspoon salt; 9 tablespoons (1 stick plus 1 tablespoon) unsalted butter, room temperature; 1 large egg yolk; 1 1/4 cups all purpose flour; 2/3 cup blanched slivered almonds; 1 tablespoon all purpose flour; 7 tablespoons sugar; 6 tablespoons (3/4 stick) unsalted butter, room temperature; 1 large egg; Powdered sugar (optional)