Combine the hot water and saffron, and let sit for 10 minutes to soften the saffron.
In a mixing bowl, beat together the saffron water, milk, sugar, butter, salt, egg, yeast, 2 cups of the flour.
Add enough of the remaining flour to make a soft dough.
Knead the dough (for about 15 minutes by hand, 12 minutes in an electric mixer, 90 seconds in a food processor, or in your bread machine using the dough cycle), then set it aside to rise until puffy (but not necessarily doubled in bulk), about 2 hours.
Punch the dough down, and let it rest, covered, for 10 minutes.
Divide the dough into 16 pieces, and shape each piece into a ball.
Place the balls fairly close together (but not touching) in a 12- inch deep -dish pizza pan or 9 x 13-inch pan, cover them, and let rise for 1½ hours, or until they're puffy.
Glaze the buns with the mixture of beaten egg white and water, then sprinkle them heavily with pearl sugar.
Bake them in a preheated 375℉ (190℃) F oven for 20 minutes, or until they're golden brown.