Make Enriched Dough: In a stand mixer bowl, dissolve yeast and 1 teaspoon sugar in warm milk; let stand 5 minutes until frothy. Add remaining sugar, 3 tablespoons melted butter, egg, salt, and flour. Knead on medium speed for 6-8 minutes until smooth and elastic. Cover in an oiled bowl and let rise 60 minutes until doubled.

Caramelize Spiced Apples: Sauté diced apples with 1 tablespoon butter, 2 tablespoons brown sugar, and 1/2 teaspoon cinnamon in a skillet over medium heat for 4 minutes until tender-crisp. Remove from heat and cool completely.

Roll & Slice Accordion Layers: Roll risen dough into a 12x20-inch rectangle on a floured surface. Brush with remaining 2 tablespoons melted butter, sprinkle with brown sugar and remaining cinnamon, and scatter sautéed apples evenly. Cut into 6 strips lengthwise, then cut crosswise into 4-inch squares.

Stack & Proof: Stack squares in groups of 4-5 and arrange vertically accordion-style in a parchment-lined 9x5-inch metal loaf pan. Cover loosely and let proof 30 minutes until puffy.

Bake & Glaze: Bake at 350°F (175°C) for 38-42 minutes, tenting loosely with foil after 25 minutes. Cool in pan 10 minutes. Whisk powdered sugar, milk, and vanilla bean paste into a smooth glaze and drizzle generously over warm bread before serving.