Activate the yeast by combining warm milk, sugar, and yeast. Let sit 5-10 minutes until foamy.
Mix in eggs, softened butter, and salt. Gradually add bread flour and knead 8-10 minutes until smooth and elastic.
Place dough in a greased bowl, cover, and let rise in a warm place for 1-1½ hours until doubled in size.
Prepare filling by melting butter and mixing brown sugar with cinnamon. Set aside until dough is ready.
Punch down dough, rest 5 minutes, then roll into a 12x8-9 inch rectangle. Brush with melted butter, sprinkle cinnamon-sugar evenly, leaving a 1-inch border on one short edge.
Roll tightly from the long edge into a log, seal the edge, and place seam-side down in a greased 9x5 inch loaf pan.
Cover and let rise for 45-60 minutes until dough rises about 1 inch above the pan rim.
Preheat oven to 350°F (175°C). Brush the risen loaf with egg wash.
Bake for 30-35 minutes until golden brown and internal temperature reaches 190-200°F (88-93°C). Tent with foil if browning too quickly.
Rest in pan for 10 minutes, then transfer to a wire rack to cool completely for at least 1 hour before slicing.
Optional: whisk powdered sugar, milk, and vanilla for glaze. Drizzle over cooled bread and let set for 5 minutes before serving.