Mixing & Kneading by Mixer
In the bowl of a stand mixer, combine all the dry ingredients: flour, yeast, and salt. Using a dough hook, add the wet ingredients—milk, condensed milk, and egg—to the dry mixture at slow speed. Mix for about 30 seconds to 1 minute until the dough begins to come together and forms a cohesive mass. If any flour sticks to the sides of the bowl, use a rubber spatula to scrape it down.
Increase the mixer speed to medium and start adding the softened butter, one piece at a time. Allow each piece to fully incorporate before adding the next. Continue mixing until the dough becomes smooth, elastic, and completely pulls away from the sides of the bowl.
Extra Kneading by Hand
Transfer the dough to a lightly floured surface (about 1 tablespoon of flour). Begin kneading by hand to form a rough ball. To do this, gently fold the farthest edge of the dough toward the center and press it down with the heel of your hand. Rotate the dough 90 degrees and repeat the folding and pressing motion. Continue this process for about 1 to 2 minutes until the dough becomes smooth and round. If the dough becomes sticky, you can lightly sprinkle more flour as needed.
First Proofing
Place the smooth, round dough (seam side down) into a lightly greased large mixing bowl. Cover the bowl tightly and allow the dough to rise until it doubles in size, which should take about 1.5 to 2 hours. This first proofing time is typical for most bread or dinner roll recipes.
Shaping
Once the dough has proofed, punch it down to deflate it, then transfer it to a lightly floured surface. Use your hands and a rolling pin to press the dough into a square or rectangle, making sure the length fits the size of your chosen baking pan.
Next, pick up the edge of the dough closest to you and carefully roll it away from you, forming a cylinder. Tuck the sides in as you go and pinch the seam tightly when you reach the end.
Using a serrated knife or a sharp knife, slice the cylinder into pieces of even thickness.
Second Proofing
Place the dough pieces neatly into a lightly greased baking pan, ensuring the seams are facing down. Cover loosely with plastic wrap and let the dough rise again until it nearly doubles in size, about 1 to 1.5 hours.
Baking
Preheat the oven to 350°F (175°C). Lightly brush the top of the proofed dough with the egg wash mixture. Bake the bread for 35 to 40 minutes, turning the pan halfway through the baking time for even cooking.
Once the bread is baked, remove it from the oven and brush the top with the condensed milk glaze while it's still warm.
Allow the bread to cool completely to room temperature before serving.