In the bowl of a stand mixer, combine the flour and yeast. Then, add the lukewarm milk and mix well. Cover the bowl with plastic wrap and let it rise in a warm place until it doubles in volume and looks bubbly (1h).
Place the bowl into the stand mixer fitted with a hook attachment. Add the eggs, flour, sugar, and salt and mix on low until the dough has formed (it will look gritty). Scrape the sides and the bottom of the bowl with a rubber spatula and switch to medium-high. Knead for 10 minutes or until the dough is shiny, silky, looks hydrated, and is a little bit sticky to the touch.
Lower the speed to medium-low and start adding the butter, one tablespoon at a time. Don’t add another portion until the previous one has been incorporated into the dough. The whole process will take approximately 10 minutes. Scrape the bottom and the sides of the bowl and remove the dough from the hook a couple of times during the process.
Once all the butter is in, knead the dough on medium-high for 15 minutes or until you can stretch a small piece of it into a square, creating a film thin enough for light to pass through. The dough should not tear at all or tear just a little bit only on the edges while performing the so-called windowpane test.
Transfer the dough to a large bowl lightly greased with oil. Cover it with plastic wrap and leave it in a warm place to proof for 30 minutes. Then, place it in the fridge for 2 hours or until well chilled and doubled in volume. If planning to bake the next day, keep it in the refrigerator overnight.
Remove the dough from the fridge, punch it down to deflate it, and place it on a lightly floured surface. Press down with your hands, forming an approximately 11" by 7" (28cm by 18cm) rectangle.
Cut lengthwise into three even lines and roll them into ropes. Braid them, seal the ends, and tuck them under. Place the braided dough into an 8" by 5" (20cm by 13cm) loaf pan greased with butter. Cover with plastic wrap and a kitchen towel and leave to proof for one hour, or until doubled in volume and springy to the touch.
While the dough is proofing, preheat the oven to 375F (190C).
When the dough has risen and the oven is hot, brush the top of the loaf with an egg wash (read notes about egg wash) and sprinkle flaky sea salt on top (optional).
Bake on the lowest ⅓ of the oven for 20 minutes. Then, rotate the pan and cover it loosely with a piece of foil. Bake for additional 15 minutes or until the internal temperature is 190F (88C). The top should be a deep brown color and the bread should sound like it’s hollow inside when you tap on it.
Remove from the oven and let it rest in the pan for a few minutes. Then, remove it onto a cooling rack. Serve slightly warm!