Tip the water into the bowl of the standing mixer. Whisk in the yeast and the sugar. Let the yeast proof (become foamy) for 5-10 minutes. Then whisk in the salt, the 4 beaten eggs, and the melted butter. Pour the flour on top. Knead at low speed until the flour is incorporated into the wet ingredients -- about 2 minutes. Then increase the speed to medium, and knead until a soft, elastic dough develops -- 7-9 minutes.
Form the dough into a ball, and then place it, seam-side up, in the greased mixing bowl. Flip the dough to grease the other side. Cover with plastic wrap ("cling film"), and place the bowl in warm location until the dough doubles in volume -- 90 minutes to 2 hours.
Gently deflate the dough, and then transfer it to a non-floured work surface. Cut the dough in half. Form each half into a loaf, and place in the prepared loaf pans. Cover with plastic wrap, and let rise until the dough just exceeds the rim of the pans -- 30-45 minutes. Meanwhile, preheat the oven to 400°F.
Before baking, brush each loaf with the egg wash. Then bake in the preheated oven until the loaves color attractively -- about 30 minutes. Cool the loaves in their pans for 10 minutes, then unmold onto a wire rack. Permit the loaves to cool to room temperature before slicing and devouring them.