In a small microwave-safe bowl, heat ⅔ cup milk on high in 10-second intervals until an instant-read thermometer registers 110° to 115°.

In the bowl of a stand mixer fitted with the paddle attachment, combine warm milk, 1 tablespoon sugar, and yeast. Let stand until foamy, about 10 minutes.

Add Milk Roux, 3 cups flour, ¼ cup melted butter, 1 egg, salt, and remaining 3 tablespoons sugar to yeast mixture; using the paddle attachment, beat at low speed just until combined, stopping to scrape sides of bowl.

Switch to the dough hook attachment. Beat at low speed for 3 minutes. Increase mixer speed to medium-low, and beat until a soft, smooth dough forms, 6 to 8 minutes, stopping to scrape sides of bowl; add up to remaining ¼ cup flour, 1 tablespoon at a time, if dough is too sticky. Cover and let rise in a warm, draft-free place (75°) until doubled in size, 40 minutes to 1 hour.

Line a large baking sheet with parchment paper.

Punch down dough; let stand for 5 minutes. On a lightly floured surface, roll dough into an 18x10-inch rectangle. Starting at one long side, tightly roll up dough, jelly roll style, and press edge to seal. Place on prepared pan, and form into an oval; pinch ends to seal.

Cover and let rise in a warm, draft-free place (75°) until doubled in size and dough holds an indentation when poked, 1 to 2 hours.

Preheat oven to 350°.

In a small bowl, whisk together remaining 1 egg and remaining 1 tablespoon milk. Brush egg wash on top of dough.

Bake until golden brown and an instant-read thermometer inserted in center registers at least 190°, 25 to 30 minutes. Brush top of warm cake with remaining 1 tablespoon melted butter. Garnish with sanding sugars. Let cool completely before serving.