FOR THE DOUGH:
1 (¼-oz.) package active dry yeast
¼ cup sugar
¾ cup milk, heated to 115°
½ tbsp. kosher salt
4 tbsp. unsalted butter, melted, plus more
2½ cups flour, plus more
FOR THE FILLING:
1 cup walnut halves, toasted
½ cup sugar
4 tbsp. unsalted butter
2 tbsp. milk
1 tsp. ground cinnamon
2 egg whites
1. Make the dough: Combine yeast, 1 tbsp. sugar, and half the milk in the bowl of a stand mixer fitted with a paddle attachment; let sit until foamy, about 10 minutes. Add remaining sugar and milk, plus salt, butter, and egg; blend. With the motor running, slowly add flour; beat until smooth. Cover with plastic wrap; set in a warm place until doubled in size, about 1 hour.
2. Make the filling: Purée walnuts, sugar, butter, milk, and cinnamon in a food processor into a smooth paste. Beat egg whites until stiff peaks form; fold in walnut paste.
3. Grease a 9" x 5" x 2¾" loaf pan with butter. On a lightly floured surface, roll dough into a 10" x 4" long oval about 1/16" thick. Spread dough with walnut mixture. Starting from one narrow end, roll dough into a tight cylinder. Trim ends and transfer to pan; set in a warm place until doubled in size, about 1 hour.
4. Heat oven to 350°. Bake until a toothpick inserted in middle comes out clean, about 1 hour. Let cool.