Place the warm milk, yeast, sugar, eggs, butter in the bowl of an electric mixer fitted with a dough hook attachment. Stir at low speed.
In a large bowl add salt and flour together. Gradually add the flour to yeast mixture; and turn the mixer speed to medium-high and continue mixing until the dough comes away from sides of the bowl and forms a slightly sticky ball.
Dump the dough out onto a floured surface or a silicone mat and knead by hand for a minute, until the dough is smooth and elastic. Shape the dough into a ball. Lightly brush a large bowl with butter. place the dough. Turn dough over so that the top is also lightly greased. Cover the bowl with plastic wrap or a kitchen towel. place the dough in a warm draft free place and let it rise until doubles in volume (it should not spring back when pressed), About 1 hour.
Remove dough from bowl and punch down . Turn dough out onto a lightly floured surface and knead for 4 minutes or until the bubbles are out of the bread.
Divide the dough into 2 equal portions; or cut in small pieces about 60 grams each or two large breads.
Butter a baking tray .
Roll out the pieces making a long rope about 12 to 15 inches long. Pinch the ropes together at one end and tuck the ends under. Then, begin braiding by crossing the right rope over the center rope. Then, cross the left rope over the center. Continue alternating, right and left over center, until the braid is done.
Place the breads on butter and floured baking tray and place the breads and let it rise for 40 minutes or until doubled in volume.
Brush the bread with egg wash mixture gently to avoid lowering the breads.
Preheated oven 180 degrees, bake 350 F 20 to 25 minutes . Remove out of the oven and brush well with the sugar glaze and finally sprinkle on the shredded coconut.