In a small bowl, combine room temperature milk and active dry yeast. Let stand for 5-10 minutes until foamy, indicating the yeast is active.
In a large mixing bowl, whisk together the yeast mixture, sweetened condensed milk, egg, and softened butter until well combined and smooth.
Gradually add flour and salt to the wet ingredients, mixing after each addition. Once a shaggy dough forms, turn onto a lightly floured surface and knead for 8-10 minutes until smooth and elastic. The dough should spring back when gently pressed.
Place dough in a lightly oiled bowl, cover with plastic wrap or a damp kitchen towel, and let rise in a warm spot (around 75°F) for 1-1.5 hours or until doubled in size.
Gently punch down the dough and divide into 3-4 equal portions. Shape each portion into a tight ball by pulling the edges toward the center and pinching to seal. Place seam-side down in a greased 9x5-inch loaf pan.
Cover loosely and let rise again for 45 minutes, or until the dough reaches about 1 inch above the rim of the pan.
Preheat oven to 350°F. Position rack in the center of the oven.
Whisk egg yolk and milk together for the egg wash. Gently brush the top of the risen dough, being careful not to deflate it.
Bake for 25-30 minutes, or until deeply golden brown on top and the bread registers 190°F on an instant-read thermometer. If browning too quickly, tent with foil.
Remove from oven and let cool in the pan for 10 minutes. Turn out onto a wire rack to cool completely.
While still slightly warm, prepare the glaze by whisking softened butter and sweetened condensed milk until smooth. Drizzle or spread over the top of the bread.
Allow glaze to set for 5-10 minutes before slicing. Best served same day but can be stored in an airtight container for up to 3 days.