Chocolate Pecan Pie Babka

Name: Chocolate Pecan Pie Babka
Ingredients: 8 tablespoons (1 stick) unsalted butter or margarine, divided; 1/4 cup lukewarm water; 1 (1/4-ounce) packet active dry yeast (2 1/4 teaspoons); 1/4 cup plus 1 teaspoon granulated sugar, divided; 2 cups all-purpose flour, plus more for sprinkling; 1 large egg; 1 large egg yolk (save the white); 1 teaspoon vanilla extract; 1/4 teaspoon kosher salt; 1 1/2 ounces bittersweet chocolate; 2 tablespoons unsalted butter or margarine; 1/4 cup packed light brown sugar; 3 tablespoons light corn syrup; 1/2 teaspoon vanilla extract; 1/8 teaspoon kosher salt; 1 cup pecan halves; 1 large egg white